Suppose we want to choose 5 objects, without replacement, from 16 distinct objects.

Easy. 

When wanting to choose something from a group we use the choose function which states:

n!/r! (n-r)!

So applying this to your problem we get 16!/5!*11!

This simplifies to (16*15*14*13*12) / (5*4*3*2*1)

So the answer should be 4368 if I'm not mistaken.