Its awesomeeee here

Why did you ask under your username awsomeee? 

the only difference is how many b***s are in each box.

0,5

1,4

2,3

3,2

4,1

5,0

That is 6 ways.

I'm assuming here that we can have an empty box.....since the boxes are indistinguishable, n b***s in the first box and 5-n  b***s in the second box is the same as 5-n in the first and n in the second.

So

Choose 5 b***s in the first box and none in the second  = 1 way to do this

Choose 4 of 5 b***s to go in one box and the remaining one in the second   =  C(5,4)  = 5 ways

Choose 3 of 5 b***s to go in one box and the remaining two in the second  = C(5,3)  = 10 ways

So........1 + 5 + 10   =  16 ways

To see the logic of this........suppose that the boxes are identifiable.....then, we have 2⁵ ways to distribute the b***s since each ball can go into one of two boxes. But, if the boxes are idistinguishable, the order doesn't matter so the total ways =  2⁵ / 2!   =  32/2 =  16