How many 5 numbers combinations can you make from the numbers 1 to 22 and what are they?

Assuming you are using "combinations" in the mathematical sense where order doesn't matter (if order does matter it would be "permutations"), there are 22C5 = 22!/5!17! = 26,334 possible combinations of 5 numbers from 22.

They start {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 4, 7}, ... and end ... {16, 19, 20, 21, 22}, {17, 19, 20, 21, 22}, {18, 19, 20, 21, 22}; I'll leave the 26,328 combinations in the middle for you to list.