May 31st to June 5th is the 15th annual Gay Day week in WDW. I've never been that week so I'm not sure how crowded it is. I'm also not sure if they spend the whole week at the parks or just, Saturday, June 4th, which is Gay Day at the Magic Kingdom so I'm assuming that day might be pretty crowded. Maybe others who have been at that time can tell you what to expect.