This question is an example of a "combinations" question, where you want to make a selection but the order does not matter. On this one we're trying to do 10 choose 5, meaning that the formula you want to set up is
C(10,5) = 10! / 5!(10 - 5)! = 252
So there are 252 different ways that you could pick any 5 members out of a group of 10