I don't believe I have. However, I realized that the only 3 possibilities for between 4 and 6 occurrences for choices A-E with 25 trials are {5,5,5,5,5}, {5,5,5,4,6}, or {5,4,6,4,6}. Should this help me in any way?
I suppose I could do p(5,5,5,5,5) + all permutations of p(5,5,5,4,6) + all...