I enrolled DS4-almost 5 in a small private kindergarten with a December 31 cut off this year (circumventing the public school's August cut off), and it has been an unmitigated success, but you might have a hard time finding a school willing to go all the way out to a May birthday. Remember, most kindergartens are going to have a lot of 6 year olds in them, and the difference between a young 4 year old and a 6 year old is huge. The school my son is at is able to make it work only because there are less than 10 kids in the class and everyone receives a lot of individualized attention (including things like help in the bathroom if they occasionally need it). If my only choices had been another year of preschool vs. early enrollment in our overcrowded public school, I would have kept DS in preschool.
I would go to the schools you're considering, observe the kindergarten classes and try to imagine your child fitting in there.