The question boils down to how many ways can you fill three boxes with five objects. We don't care which object is in which box or which box is which. So you just need to list the sets of three positive integers that add up to five:
{5,0,0} {4,1,0} {3,2,0} {3,1,1} {2,2,1}
This totals to 5 sets, meaning there are 5 ways to distribute the objects.
