Hi Aimee and thanks so much for visiting the Disney Parks Moms Panel!
When my kiddos were 7 and 5, our double stroller didn't make it to Walt Disney World Resort until the 2nd evening of our vacation. It racked up some additional frequent flyer miles by touring various cities in both Texas and Florida (oops). So - for two days, we were without a stroller. It was doable but their little legs were so tired by the end of each day.
If you are going to visit the theme parks for a short period of time before heading to your Resort hotel, I think you will be fine. If you plan to spend the majority of the day in the theme parks, I would suggest bringing your stroller with you. If nothing else, you can use it to carry your backpack.
A few pieces of advice based on our experience: 1.) Take a small blanket or towel to cover the seats of the stroller during the day when you are on an attraction as the stroller can get hot in the sun. 2.) Take a rain cover if you have one. While we didn't always need it, our stroller rain cover was a life saver on a couple of occasions. 3.) Put some kind of brightly colored or unique identifier on your stroller to help find it faster. When you are inside an attraction, your stroller may get moved to accommodate others as Guests arrive and/or move on to other parts of the theme park. Regardless of the style and brand of stroller you have, during your visit to Walt Disney World Resort, it will appear that virtually every other family has the same stroller.
5 and 6 are such great ages and I know you are all going to have an amazing time! My "expert" 9 year old recommends
The Barnstormer and
Dumbo The Flying Elephant for your kiddos. Enjoy your magical vacation!