We have been probing space for a while now, and we are definitely capable of establishing a settlement on a separate celestial body, such as the moon, given the resources required to do so. Spreading our species across multiple moons and planets would greatly increase our chance of survival and decrease our chance of bringing about our own extinction, and inhabiting other solar systems would allow us to outlast our sun. As for the other species on our world, they aren't a reliable way to judge our chance of survival. Many have gone extinct, but plenty of those aren't completely gone, still alive in the form of their evolutionary descendants. Creatures evolve and adapt to meet their needs, and if anything we are more capable of doing so than other other species on Earth. In 5 billion years, should we play our cards right, we may very well still be alive as a species, or we may have given birth to a greater species of human that took our place after what we current consider humanity has faded away.
Face the facts. The first life on Earth was about 3 billion years ago. Think about how much life has evolved and how many species have gone extinct. Humans are no different. Yes, we are one of the most intelligent species. But we cannot stop our own extinction. Also, the way things are going, we will cause our own extinction. We have already caused so many living things to die.