No, it won't. Earth will either be a scorched planet or will be engulfed by the Sun. And it won't take those 5 billion years either for life to vanish from Earth. We're currently near the inner edge of Goldilocks zone (Mars is just a bit outside of the outer edge) and we have only like 500 million years. Either start colonizing other planets or we die, there nothing in between (assuming we don't destroy ourselves meanwhile).