We went to Disney when my sister was 5 and she didn't use a stroller. She was fine until about the 4th park day in a row before the whining and complaining got to be too much, but that was luckily our last day. We would first get to the parks around 11 or noon, but stay late/relatively late.
I took my son to Universal's Islands of Adventure when he was 5 with no stroller. We had lunch at CityWalk, then went to the park until about 7:30pm. You should be fine as long as you structure your day so you aren't walking all day and don't try to do parks day after day, no rest day.