this is the IOIB (identical Objects, Identical Boxes) problem. According to the problem, each box has at least one DVD.
Let each box be labelled, B1, B2, B3, B4. B5.
$\therefore$ We need to find the number of partitions of 8 into 5 parts where $B_{i}$ $\geqslant $ 1
There are 3 ways
8 = 1+1+1+1+4
8 = 1+1+2+2+2
8 = 1+1+1+2+3
(NOTE: since all the objects and boxes are same, all other permutations of the partitions will be same)
Thus, there are 3 ways to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD.