But there would be drawbacks to living in a society where the average lifespan is so long, like stagnation of society.
The only people eligible for 5000 yrs lifespan ought to be compulsively creative types like Michelangelo. There are not many (actually, very few) of those, but with them stagnation would be unlikely. The lesser mortals should remain mortal.
We should be thankful that we have a limited lifespan. It gives us motivation to accomplish something. So everyone, get off your butts and accomplish something!