This is very similar to example 11 on page 379:
Since it explicitly says "No simple close formula exists for this number [indistinguishable objects and indistinguishable boxes]," the best way to go about the problem is simply list the solutions.
Box 1: 5 4 3 3 2
Box 2: 0 1 1 2 2
Box 3: 0 0 1 0 1
So, the answer is 5.
