It all depends. Obviously you need a stroller (or strap-on carrier) for the baby, but as for the older child, do you plan to tour all day, every day, or will you take a mid-day break? Is your 5-year-old healthy and fit? Will you be keeping him/her up very late? Will he/she be getting adequate sleep?
We never needed a stroller for our 4 and 6-year-olds, but we never toured for more than 5 hours at a time, and did our best to approximate the kids' normal sleep schedule. (Each day, we would: tour from rope drop - lunchtime, head back to the resort for 2-3 hours of napping, swimming and relaxing, and then go back to the parks from about 4pm-9pm). With that schedule and a good touring plan that allowed for plenty of breaks and leisurely meals, we nonetheless covered practically everything in every park in less than 6 days with no stroller, no meltdowns and no whining to be carried at the end of the night (except maybe by me).