Photo copyright Walt Disney Company.
Does this mean you need to pack 376 diapers and 4000 wipes for a five-day trip? I've definitely come close to filling up an entire suitcase with baby supplies. The bonus is that when you leave, you'll have extra space your luggage to put souvenirs. But if you have a car you'll be happy to know that there's a Super Target and a Walmart just a few miles off Disney property; they have everything your local stores have.
You can even order your usual diapers from services like Garden Grocer and We Go Shop or you can send diapers to your resort from any of the companies you usually buy from (Target, directly from the company, etc.). Most resorts, including those on Disney property, will hold items for you until you pick them up, but make sure you ask ahead of time. Because buying from the source and shipping to your resort is so easy, I don't normally recommend any of the Orlando based disposable diaper delivery services. They're a great idea--some of them even "bundle" diapers and wipes for easy trips to the park--but they're so expensive, I think you're better off getting your diapers on your own.