In this case, case work might just be easier.
Each number shows the number of balls in that box.
0 0 5 1 way
0 1 4 5 ways
0 2 3 10 ways
1 1 3 10 ways
1 2 2 15 ways
1+5+10+10+15 = 41
Hopefully it's 41. :))
=^._.^=
Edit: The more I think, the more unsure I hate this answer. There has to be a nicer way to solve this. Casework wasn't too bad since the numbers were small, but I don't like using it too often since calculation mistakes occur. I hope someone else also answers.