Hiya, Kristin!
Of course, I think any time is a great time to visit
Walt Disney World, but for lighter than normal crowds, I always say it's best to go right after a school holiday. In your time frame, I'd be looking at the week before Thanksgiving or just after, and then again early to mid-January (just after Christmas and New Year's). Always keep an eye on the
runDisney events, which can impact part of January, and avoid school holidays like Martin Luther King Day or President's Day Weekend.
As far as accommodations for a family of five, you have a ton of options.
Disney's Art of Animation Resort has family suites that sleep up to six, including a separate bedroom for mom and dad. With a kitchenette, you can prep and serve quick meals or snacks from the microwave.
You'll find comfortable accommodations for five at
Disney's Port Orleans Resort - Riverside, with two double beds and a pull out single. With stately mansions and rustic cottages, you'll find yourself on the bayou, just across from a breakfast of beignets and Mardi Gras.
All of the deluxe resorts will accommodate a family of your size. My girls would say their favorite is
Disney's Animal Kingdom Lodge. You can book a savanna view room, but even if you don't, you'll have access to view some of the most majestic African animals, enjoy incredible food, and see one of the largest collections of African art outside of the African continent.
Enjoy planning for your upcoming vacation magic!
Anna