The problem is not clear . . .if I throw N cubes, what is the probability
that exactly 5 of the numbers: 1,2,3,4,5,6 will appear?
What do you mean by "exactly five of the numbers"?
Do you mean, for example, that only 1, 2, 3, 4, and 5 appear (and the 6 does not)?
Do you mean a "five of a kind" (a Yahtzee)?