The 5 year old is already 42-43 inches right now and will be taller by next summer. Kids hit 40" by around 4 years old. The rides I mentioned are ones he can do if we went today, except for Dudley but he might hit it by then summer.
As I said, this change may lead us to bringing a stroller which feels odd. Admittedly, we do tend to have at least 1 if not 2 backpacks for our party (8 people) because we like to carry frozen water bottles, snacks, sunscreen, wipes, ponchos, etc. I'm not talking huge backpacks, but ones that are too big for the small lockers. Oh, also the kids have wands.
As others have mentioned, it is not a problem at Disney since we can always carry the bags onto the rides.