5
B***s do not matter but boxes matter
we have following pssible scenarios: 4-0, 0-4, 3-1, 1-3, 2-2
You can consider it like Box A gets 0-4 b***s(5 possibilities) and Box B gets the rest.
Mathemathical explanation may be C(4,2) - 1 (1 for (2,2) scenario which both boxes have same amount and do not have to count the scenario that b***s switch and get (2,2) again)