Our 4-year-old never needed a stroller in Disney, but then again, we toured in 5-hour stints (ropedrop to lunchtime, and 4pm-9pm or so) with a lengthy nap break in between (my daughter was past the napping age, but the whole family took daily naps anyway when in WDW and no one had trouble getting to sleep!).
I'd take your 5-year-old on some mall-walking, museum or festival excursions to test his/her stamina, and compare it to what you expect to be doing at WDW. If you can avoid lugging around an extra/second/larger stroller, I'd do so at all costs. You can always rent one on-site or from a local company if you discover you really need one. Just bring the phone numbers with you to make it easy.