5. Let S(n, k) be the number of equivalence relations on the set {1, 2, ..., n} with exactly k (non- empty) equivalence classes. Prove that S(n, k) = kS(n - 1, k) + S(n - 1, k - 1) for all integers n and k such that n > k > 1. (S(n, k) are sometimes called Stirling numbers of the second kind.)