I have no proof that Hashirama didn't get old? Or that his cells combined with Madara's chakra couldn't have created some form of enhanced longevity? If so, I do have evidence; the Uzumaki clan. They possessed a powerful chakra that greatly enhanced their lifespans, giving their village the nickname of 'The Village of Longevity'. Given the fact that Hashirama's chakra and physical energy dwarfs theirs, demonstrated by the fact that no one is running around with an Uzumaki's face growing off their body, it's hardly a leap of logic to guess that Hashirama might have had an extraordinarily long life-span. As for the Sage, yeah, he got old, but we have no idea how old he actually was.