What are the 5 different ways to split up the 36 students in the class?

Answer 1

Your question makes no sense. There are more than 5 ways to split up 36 students,
here are a few:
(1,35), (2,34), (3,33), ....
If you have groups A and group B , there would be 35 such splits

If you meant: How many groups of 5 students can you choose from 36, that would be:
C(36,5) = 36!/(5!31!) = 376,992

If you also care about the order in which they are picked,
multiply 376,992 by 5!

See how critical it is to properly word your question?

Answer 2

If you mean the five ways to factor 36, those would be
1x36
2x18
3x12
4x9
6x6