The Disney resorts are quite strict about the maximum capacity of their rooms. However, there are a number of lodging situations at WDW that will accommodate your family -- some at every price range.
Your first step in your research is to check out the page on the WDW website with lodging ideas for parties of five or more, found
HERE.
The least expensive option is likely to be a Family Suite in the All Star Music resort. These two-room suites sleep up to six people and include a small kitchenette. The Family Suites also have two bathrooms, which is a HUGE plus in my book.
Another good option is a cabin at the Fort Wilderness campgrounds. These also have two rooms, plus a full-sized kitchen and outdoor space, but only one bathroom.
Beyond that in price are villa rooms and suites.
When my family of five (me, hubby, twin daughters, older daughter) goes to WDW we most often stay in a villa-style room. However, when we travel away from WDW we have found that we almost always have to get two rooms to fit our group. If you do decide to go the two-room route at WDW, you should know that there are rooms with internal connecting doors at all of the Disney hotels.
My suggestion would be to call Disney reservations at 407-W-DISNEY to discuss availability and pricing for each of the different options.
Good luck with your planning.