Renee,
We are a family of 5 as well, so I am familiar with this concern! You will have a number of options available to you, though admittedly most are in the deluxe category. Disney does have a web page devoted to larger traveling parties, but a few options are not on that list.
Large Party Sizes
By category:
Value Resort - All-Star Music has family suites! These were created by combining two rooms each, and will have plenty of room for your family. They can accommodate up to 6 plus a baby in a crib.
Moderate Resort - Port Orleans-Riverside has rooms that will sleep 5. Select rooms in the Alligator Bayou Section have a trundle bed that will sleep a 5th person. This trundle bed is best for children - it would be a bit small for an adult.
Fort Wilderness Cabins will also accommodate your family, and they offer the added benefit of including a full kitchen!
Coronado Springs also has 1-bedroom suites available that will fit your family, but be forewarned that this is an expensive choice. While it is a beautiful resort, for that amount of money I would stay elsewhere.
Deluxe Resorts - All deluxe resorts, as well as the Dolphin (which is not Disney owned but is on DIsney property) will accommodate your family of 5. We just returned from the Grand Floridian last month and we had a lovely room with a daybed in it that my daughters loved.
Hope that helps!