What are the most promising areas of research for the next 5 years?

Sorry, but I think this a quite stupid question! 
With these types of questions, funding agencies and decision makers will quite likely judge the answers as "realistic" and put lots of money into these fields (that are already over-funded) with as a result that lots of "less optimal, not to say bad" research projects will be funded. You have just to look for some older "hot topics" ... which clearly show what I predict. I would say, the most important fields are those in which little scientists are working because believed not important or too basic. 

Just to cite two world-class scientists, Paul Berg & Maxine Singer (Inspired Choices (1998) Science 282: 873-874 ) : —it seems that the fringes, not the mainstream, are the most promising places to discover revolutionary advances. Attempts to program the direction and tools of genetic research could not have foreseen the diverse sources from which progress resulted. The lesson is that those who attempt to program future fundamental research, however well motivated by medical, agricultural, or social needs, are likely to divert researchers from the fringes where the most promising discoveries are often made.--   

Think of PCR, think of GFP, both resulting from the fringes and you are in the type of really important research !!! 
Look for the fringes!

I tried to look at these in terms of contributions/drawbacks and whether research is predictably low-hanging in order to be realized within the time frame expressed in the prompts.

1. Climate change is an area that comes closest to an existential risk on the list. We need immediacy on this issue though convincing the world we should work cooperatively toward the goals of maintaining a healthy planetary environment for some or all the stakeholders (plants through humans) may make this one of the last issues humanity faces with most of the findings from research becoming little more than historical artifacts.  

2. AI and machine learning come next though it depends on how we define machine learning per se. I enjoy letting a program run near-infinite iterations of complex algorithms to validate the importance of variables. I am unsure if I want to turn this decision over to AI whereby the inclusions of variables are left to a program. Some reasonably well-intentioned and fairly well-educated people have concerns about AI as an existential risk as well. I remain unsure when it crosses over from a tool to a risk. Advances in AI seem nearly inevitable and whether this become triggered by a discovery or slowly develops over time is the challenge. However, to learn to control AI we must know AI.

3. Neuroscience and brain-computer interfaces as far as I understand the fields only become problematic when they approach dehumanizing features and/or when they are available to selected classes in our society. After studying the caste systems throughout history this could become a major problem. Of course, the level of benefits this may have in terms of resolving health issues would need to be a counterbalance. Dehumanization is a huge problem. Once dehumanized a population is not easily re-humanized as history has demonstrated. Significant developments in this field are predictably likely.

4. Genetics and personalized medicine are rich-poor issues for me. Those who benefit will be those who can afford to benefit for a host of reasons. This will be occurring because the drivers are deeply entangled in our current medical-industrial complex. 

as per my understandings we can not limit the horizon of research. the beauty of the research is to explore that is hidden, unseen and beyond our thinking . No doubt these fields are very important but considering the pace of technology coupled with climate change, there will be requirement of new types of agricultural practices and food as well. marketing channels will be in shape and design and what about health scenario as we all have recently faced the global epidemic of Covid 19

All four. Overall, these areas of research are likely to see significant progress and breakthroughs in the next five years, although it is important to note that scientific advancements can be unpredictable and there may be other areas such as Biotechnology and Bioengineering and Quantum Computing that can see unexpected breakthroughs.

DREADD, optogenetics and genetic sensors (like genetically-encoded calcium indicators). 

Research always is based on a critical issue that we are trying to resolve or advancement of a technology to ease our work. 
 So we may not be able to pin point this in to one or two direction. 

However Health being the most critical game player in humans life, more advanced medical aspects is a key research target. I'm in molecular pathology field, there is a lot of potential and untapped territories in genomics , which can be aimed at prevention and better prognosis of various disease conditions from cancer, infectious diseases and non communicable diseases. 

Climate change and antimicrobial resistance

AI, SDGs especially renewable and affordable zero carbon  based energy generation, air and water purification, health and well-being 

I personally think all four have equal importance. 

It apparently seems that climate change and microbiology promising for life sciences. Also, we could say a new area microchem which is the combination of bacteria and chemicals. It leads to lots of opportunities in order to create a green world - sustainability. And, probably food and friendly products. My opinion on that area, all other scientific challenges might be served it.    

I think the first research priority area especially in low and middle income countries should be in climate change and the environment. Currently, there are so many disasters happening in these countries and many human lives and property  are being lost due to these effects of climate change. So, we need more research in climate change and the environment whose findings may inform policies in this area. The second research priority area should be on AI and ML given that we're in the fourth industrial revolution and we're all supposed to embrace digital technologies. However, we need research in AI and ML so that we are able to reduce the technological divide between developed countries and developing countries. 

1,2,and 4. AI and brain-computer interface are fields where breakthroughs are most expected. Climate change study is one of the most needed research fields, related to it are alternative energy resources, such as geothermal energy utilization.

All four areas mentioned are important..and some of them are interlinked. For example AI can help in research related to all the other three areas, so when you think about it AI, ML probably will continue to be a priority. If you think of what is really important and more urgent for humanity in general, climate change would be my vote

(1). AI will be the driving force
(4). Neuroscience and Brain-Computer Research

Ceirtanly: Artificial intelligence and machine learning will the first, followed by Climate change and environmental science, after that Neuroscience and brain-computer interfaces and at the end Genetics and personalized medicine.
However, Artificial intelligence and Genetics and personalized medicine will also grown a lot, as we can se today

1-4 will be important moving forward bearing the interrelatedness of the topics. AI obviously will become recurrent decimals with potential to tie all areas of human existence. Thus, it is very most probable the drive for a better understanding of AI being a niche area will drive it overboard.

The sequencing of the human genome obviously has given biochemist/geneticist a tool to decipher critical areas of human existence. However, the unknown presented by proteomics remain an antidote to harness the full gains, leading to personalized medicine. Moreover, tools created through the human genome sequencing also continue to inform efforts to characterize the entire genomes of several other organisms used extensively in biological research. These efforts support each other, because most organisms have many similar, or "homologous," genes with similar functions, helping in functional analysis that may promote personalized medicine. Herein as scientist optimise molecular biology/bioinformatics, there remain a likelihood for a cross border between AI and the race to actualize personalized medicine. 

There is a race for climate change research, this has being heightened  bearing climate change consequences are very far reaching to human existence. Thus, best tools to gain net zero, carbon sequestration, adaptation and mitigations measure may need AI intervention taking into cognizance the versatility. Such may position developing countries the best probable route and to a large extent the highest prospects of being strategically positioned to reap from the benefits arising therefrom the NEW market mechanism (NMM) of the Paris agreement.

Research into neuroscience and brain computer interface, is important at this time of sensibility to mental health. Again AI will be essential to facilitate the understanding of the neuroscience-processess that are vital. To this extent the mapping of the brain with the essential transmitters are vital, moving forward.

Considering that a researcher gets ideas/inspiration from other research works, all four areas can be promising based on the type of research being carried out.  There could be several other promising areas which are not mentioned here. Hence choosing any one of these topics, or suggesting other topics may not be apt in my opinion.   

Artificial intelligence and machine learning

(1) and (2)

I think the best question would be : which of these three themes will raise as a priority in the next 5 years?
So the answer would be 3.Climate change and environmental science
It's not because the other options are not important. It is just because we need to be alive to make them work. 

 

All four fields have grown tremendously since the 1990s, and will keep or at least maintain that  growth rhythm.
Ricardo Chiesa

A.Artificial intelligence and machine learning
B.Genetics and personalized medicine

Artificial intelligence, Mental Health, Happiness, Genetics, Personalized medicine, Organ transplantation, Food safety, climate change, Long-term Impact of digital devices etc.

This is an interesting way of formulating the question, i.e. the most "promising" as opposed to asking which fields should be ranked higher in terms of their importance. As such, climate change and environmental issues are major existential challenges to the survival of our civilization. As such, any "promising" stretch or innovation to address these issues and provide solutions will be important as it may end up being a question of survival of the world as we know it. However, it is also a question of policy, regulations and human behaviour as general as these are all part of the solution to get ourselves out of the mess that we've created. That's why I think that some aspects of social sciences are also important and promising outcomes in these fields should help. There is some interesting work being done in economics in relation to the importance of incorporating the health of nature and also considering the value of considering indigenous values and knowledge.

The other fields are all interesting and promising and may end up playing important roles in how our species (and ecosystems) can adapt to this rapidly changing world.    

I think it will be:

I believe  

AI and imaging for diagnosis and prognosis 

(5) biological engineering

In my opinion, Virtualization, Data Science and connecting them with Applications via IoT, Robotics, Augmented/Virtual Reality, etc. are to be paid attention 

Genetics and personalized medicine

Climate change and environmental science

 Only the genetic question. The others will all be outdated as computer science is moving fast and will have a whole lot of new unexpected methods  within a very short time.  Especially as AI can be taught to do research without help from humans. One of the research topics which is top of the spectrum in Medical and Veterinary Science is  the endothelial system. That holds the key to  health and longevity for the human race.

I think genetics and personalised medicine is the most hot point of research in the coming 5 years. Now the concept of precision medicine is so attractive as a strategy to do intervention early enough before the clinical presentation of diseases. 

Personalized therapy
AI and ML

I would prioritize as follows:

Post translational medicine
AI
Cell Therapy
New vaccines
Global warming

In my opinion all 4 fields are growing at fast pace and will be a promising research field. 

Climate change and environmental science will be the most promising research areas for the next five years because the climate has been proven to have a direct or indirect negative impact on human health, natural resources availability, agricultural system productivity and bio-cycle, which is necessary for healthy, prosperous and standard life living.
While environmental science which is dealing with the quality of air, water, soil and other resource quality. Sustainability and pollution control is another area, particularly  to achive transition from a fossil fuel-based economy to decarbonised and circular economy. Even many of the research areas in this field are unexplored, which has a tremendous opportunity to conduct research and publish good research for food, fuel and public health safeguards.

I believe all of four. In neuroscience scientists are looking for reducing the variability of responses to treatment or modalities they use. In this field it is believed that inter-individual differences lead to differences in response to same treatment with same parameters and therefore, it is a need to individualised the treatment based on each individual characteristics. AI and genetics would be helpful in this area!
Climate changes are a major problem of the environment and to delay the destruction ability of it, it is a need to have researching in this area more than past.

And AI is growing so fast in any field including neuroscience and there is no way to exclude its effects and possible potential consequences it has. 

(1) and (4)