We have gone the last two years in early and then in mid May. There were crowds but it didn't seem crowded. This year we have plans to go end of June to early July. I want to change to May again. It is a great time to go. You'll enjoy it a lot.
The beginning of May is not very crowded at all. On some rides and attractions you may walk right on. The longer the month of May goes along the busier the parks will get. Summer breaks start, Memorial Day weekend, etc, etc. Try and go as early as possible in May. Good luck and have a great trip!
ADP