SOLUTION
Question a: The correct way to get the ways 5 colors can be chosen from 13 colors is by using the combination formula since order does not matter; We have:

Hence, the number of ways 5 colors can be chosen from 13 colors if the order does not matter is 1287 ways.
Question b: The correct way to get the ways 5 colors can be chosen from 13 colors is by using the permutation formula order does matter; We have:

Hence, the number of ways 5 colors can be chosen from 13 colors if the order matters is 154440 ways.