Please explain what I'm doing wrong!

That is seven combination 5 not seven times five. How to find the combination: 7!/(7!-5!)*5!. The ! means 7*6*5*4*3*2*1. so to simplify it you can do this: 7*6*5!/2!*5!. The 5!'s cancel out. so you are left with 7*6/2. 42/2. The answer is 21.

7C5
Supermathexpert is correct !

7C5 = 7! / [(7-5)!*5!]
What I am trying to show is that the 5! is on the bottom.

= 1*2*3*4*5*6*7 / [(1*2) * (1*2*3*4*5)]
= 6*7 / 2
=21

If you are doing it on your calculator there is a button that looks like nCr

You put in 7 nCr 5
The C stands for combinations

If you have 7 different books on a book shelf, 7C5 gives you the number of different combinations of 5 books that you can choose.

It is used in probability all the time.
Both numbers have to be whole numbers and the second one cannot be bigger than the first or it will not make sense.
I hope that this helps.