I'm actually a lot more worried about Chief's mental state than his physical health - sure, he's ageing, but it's mentioned in one of the novels that the average human life by the time of Halo often exceeds 120 years - making Chief perhaps as young as 35 by today's standards, and that's before we consider that he's spent a very great deal of time in cryogenic stasis, during which he wouldn't have been ageing at all. Indeed, between Halo 3 and Halo 4 four years passed and he spent all of that in suspended animation, meaning at the very worst he's only biologically about 43, which isn't really that old at all. Even in the modern military, soldiers are quite capable of staying fit well into their 50s, and they neither have cybernetic enhancements, suspended animation, or a life expectancy of 120. So physically, the Chief is going to be absolutely fine for a good few years yet, and possibly even longer based on whatever the Librarian did to him.
Mentally though, he's got to be a complete wreck. From his perspective, it's only been a few months since he saw Reach fall, and in that time he encountered the Flood and was almost infected by one, fought almost continuously for days on end on Halo, broke a suit of Mjolnir armour through heavy use, watched Earth get invaded by the Covenant, had a severely damaged Cortana put back into his head, watched both Miranda Keyes and Johnson die, was caught in the firing of a Halo ring, had a rampant AI directly connected to his thoughts, watched an entire space station full of civilians disintegrated, and then had his only companion die right in front of him in order to save his life - and that's not even counting getting back to Earth and discovering almost every other member of the Spartan-II programme has been killed or crippled since he last saw them. None of that can be good for his emotional health, and it's mentioned in Reach and the associated literature that Spartans often display antisocial or psychotic behaviour even at the best of times. If Chief weren't a Spartan he might well have snapped already.