The answer is that no one knows for sure as it has not been fully confirmed. However, there are a lot of theories circulating online, after Metal Gear Solid 4 took place in 2014 during that time Solid Snake was aging at a very fast pace, with every 5 years Solid Snake aging 30 years instead. According to Dr. Naomi Hunter, a genealogist specialized in nanotechnology-based gene therapy he had 6 months to live in his current condition despite being injected with Drebin’s new strain. This is further backed up by the fact that multiple characters in the game referring to Solid Snake in the past tense which may mean that he has already died.
For example, Kevin Washington, a member of Raiden’s support team within the PMC Maverick Security Consulting Inc. said “I wish I could have met him.” when talking to his group leader Raiden. It also needs to be pointed out that the Japanese version of the game Metal Gear Rising: Revengance game has a sword which contains the ghost of Solid Snake and it makes no sense for someone to be alive and have a ghost at the same time so this is, therefore, another confirmation that Solid Snake is dead.
Another thing is that the way the Metal Gear franchise is going right now thanks to Konami it may take some more time and games to be released by them for the gamers to get a proper answer of the fate of Solid Snake, with the latest installment in the Metal Gear series being the Metal Gear Survive game. It was a decent zombie survival video game but a let down of a Metal Gear video game. Konami could have done much better by releasing the game under a different name.