D&D 5E Reincarnation and maximum age

[Elderbrain]

When a PC is laid low in battle, his Druid pal can cast the Reincarnate spell on him, and he comes back to life with his memories intact but in a different body (in 5e, always a PC race). Question: Does his age change? Does his MAXIMUM age change to match his new race? Picture this: An elf that's 300 years old comes back as a human. Humans don't live 300 years! Does the new human die instantly of old age? If not, does he get the remainder of his lifespan as if he were still an elf? Is he treated as a starting human character (I.e. adult age but still young)? Seems like you could either wind up dead in a hurry (if switching from long-lived to short-lived race) or else you could become effectively immortal by just dying in battle periodically and having your Druid buddy Reincarnate you again each time. Am I missing something...?

 

[The Crimson Binome]

Previous versions of the spell would clarify that it creates a body that is a young adult for the new form, so you could use that as an effective form of immortality (if you kept repeating it whenever you got old), but druids aren't terrible prone to abusing the laws of nature like that. (And if you do that too many times, they send Terminators after you.)