Yes and no.
We could live virtually forever, if not for thousands and thousands of years by traveling the speed of light, according to your premise.
The question I ask has more to do with human physiology than physics. Either you spend 4.36 years on a spaceship, or you don't. If you claim you actually do spend 4.36 years on a spaceship, then are you claming it has some physical effect on your body to keep it from aging? Can't be.
I don't understand your premise. If you are gone 25 years, your heart has to beat so many beats per second, per hour, per year. Are you claiming that traveling the speed of light somehow changes that principle? If time slows down, are you saying we would be in such a state of suspended animation that we would live 25 years would be the equivalent to 4 years in suspended animiation?
TO me it is not a coherent premise. But it is interesting.
Perhaps I'm the ignorant one.
But I thought that was Einstein 101.
No, see, you could indeed reach a chronological age of a thousand - that is, on Earth, a thousand years have passed since your birh - while having only physiologically reached the age of thirty or so. From your perspective, on the space ship, the outside universe has sped up. From its perspective you have slowed down.
The spaceship spends 4.36 in transit - that is, an observer on Earth would watch as it moves about for 4.36 years. The passenger on the spaceship would notice considerably less time passing. It's a tricky sort of concept. But apparently true.
Traveling close to the speed of light (according to the theory of relativity, no physical object can actually travel at the speed of light) does indeed change that principle, insofar as that what takes 25 years from the perspective of everyone else outside the spacecraft, takes only (say) 4 years from the perspective of the people and things inside the spacecraft. I don't fully understand the reasons why myself, I just know for certain that that's what physicists universally accept.
Apparently there've been experiments of various kinds to demonstrate this. One of the better known (if I recall correctly) involved sending planes around the world with atomic clocks on board, and comparing them to atomic clocks on the ground. The clocks on board the planes experienced a slightly shorter (like, microseconds only) passage of time than the ones on the ground.