What is one of the key indicators of primates' adaptability?

It's interesting that you posted your question in the history section of .  It qualifies in the category of "Big History," as some have termed it.  That term was coined by the scholar David Christian, whom I met once at a conference where he was a presenter.  His idea was that we look at "history" not just as what has happened in the recorded records of human beings, but look back at all that has occurred in the history of the universe.  So the "Big History" concept incorporates the story of evolution into its account of things.

As far as your specific question, a key indicator of primates' adaptability is that you see primates living in all sorts of different regions on the planet.  Snow monkeys live in cold regions of Japan where snow covers the ground many months of the year.  Howler monkeys live in the tropical rainforests of Brazil.  And there are other primates of all sorts in all sorts of climates and conditions.  That shows the adaptability of primates to survive and thrive in various circumstances.