[AaronBrown]

If we keep the rules the same as Poker, so there is an Ace that can be high or low but you cannot go around the corner, there are N - 3 possible ranks of straights. Any card but 2, 3 or 4 can be the top of the straight. Each of the N - 3 straights can be formed 5^S - S ways. So that's (N - 3)*(5^S - S) for straights.

The flushes can be formed S*(C(N,5) - N + 3) ways.

These will be near equal when N = 3*(S + 1). The only exact case I know of is the trivial one, 1 suit, 5 ranks, every hand a straight flush.

4 suits 15 ranks is pretty close, there are 12,288 straights and 12,012 flushes. Even better is 7 suits 25 ranks, with 369,754 straights and 371,910 flushes. Those numbers include straight flushes in both counts.