Let $T = \{ 1, 2, 3, \dots, 14, 15 \}$.  Say that a subset $S$ of $T$ is [i]handy[/i] if the sum of all the elements of $S$ is a multiple of $5$.  For example, the empty set is handy (because its sum is 0) and $T$ itself is handy (because its sum is 120).  Compute the number of handy subsets of $T$.