You might be tempted to use stars and bars, however, this time the balls are not identical so stars and bars would not help.

Instead start by placing $10$ balls into the first box (how many ways can you pick the $10$ balls that will go in this box?), and then place each of the remaining $20$ balls into one of the $5$ remaining boxes (you can do this one ball at a time).

Let us know if you need additional hints for this problem. Happy New Year!