The only way you could stay in a room at the All Stars is if one of your children is under 3, they will allow him/her to sleep in a crib. You could get two connecting rooms at the All-Stars, however, which would give you an extra bathroom, and lots more room.
The only moderate which will allow 5 is Port Orleans - Riverside, in Alligator Bayou. They have a trundle bed which will sleep a child comfortably, but it is really too small for anyone over 5 feet.
The Contemporary Garden Wing rooms will sleep five very comfortable, the rooms are huge - they have two queen size beds as well as a twin sized day bed. They are the least expensive deluxe option for people who have 5 in their family.
There aren't any codes out yet for May, but they probably will be issued, as it is regular season. Keep an eye on Mousesavers.com. They always post any available codes.
Happy planning!