We have a chance that human civilization doesn't last next century, maybe even this one. We have a far closer existential threat right in front of us. If you want to feel anxious about something, try that. In practice, it won't make any difference.
Regarding time scale, 15 thousands of years ago there was no civilization, 100 thousands of years ago there were not even language, a couple of millions of years ago there were not even hominids. In that context 5 billion years (or just one, as when the sun starts to get into red giant phase life won't be possible here) is just meaningless.
In the other direction, change in our civilization is accelerating, how we went from knowing barely the continents were in, to finally have a global understanding of how it was the world, then global communications, fast travel, globalization, internet and AIs were things that happened increasingly faster. If we don't crash soon somehow. we might be able to at the very least to make self-sufficient space environments within this millennium and not be tied to a single planet.