More speculation here about exponential increases in life expectancy, with another appearance by Aubrey de Grey (see also here); the occasion for the article seems to be the Social Security debate, although I'm guessing a 5000 year lifespan would have more important (and even politically provocative) consequences than the budget deficit.
Just to point out an inaccuracy/careless statement -- the article justifies its vision of the future like this: "Since women tend to live longer than men, it's safest to imagine this astonishing life span first being enjoyed by a female." The thing is, I think the assumption that women's longer lifespan is somehow intrinsic or biological or even genetic (!) may well be wrong. I have never seen, for instance, a study comparing lifespans across people who hold employment of comparable physical difficulty, and at the same time I observe that women's lifespans have been dropping relative to men in recent years -- an indicator, perhaps, that joining the workforce is taking its toll in women's life expectancy. But whether or not this is the case, the assumption that a technology extending human life to 5000 years would be subject to the same constraints (biologic or otherwise) seems a bit heroic.