Cases:
no repeating -- 5!
2E's, 0S - 5!/2!
2E's, 1S - 5!/2!
2E's, 2S's - 3C1 * 5!/(2!2!)
2E's, 3S's - 5!(2!3!)
3S's, 0E's - 5!/3!
3S's, 1E's - 5!/3!
3S's, 2E's - 5!/(3!2!)
i think you get the basic idea, not sure if i forgot some cases
Edit: whoops someone got to it before me)
Edit 2: I did, also 1E2S, 1E3S, 0E2S