For May/June the deal is like this..
The later you go..the more schools, colleges and universities have let out and that means more visitors. It really is that simple.
The very final week of May and the first week of June is GayDays in Orlando at area themeparks and while not sponsored by Disney, it does bring about 100,000 ppl to the Orlando area (not just Disney) during that time frame.
Early May? Or even up til about the 26th? Fantastic time to go for crowds .. but again.. the later you go, the higher the crowds generally speaking.
Hope this helps,
Knox