We are looking at doing all 5 of those Utah Natl parks some time down the road, probably in September. Maybe in 2020. We've been to Grand Canyon, and Yellowstone, too, but would go back if it works into the schedule. It's a long ways from Florida!
We generally prefer to stay at private RV parks outside the parks and drive in. That would be different if the Natl park was the main destination of our trip and if we could plan far enough ahead to get a reservation.
Here's a web site about 5 parks in 5 days (I wouldn't try this with an RV):
https://utah.com/five-national-parks-five-days
Any comments about Zion, Arches, Canyonlands, Capitol Reef and Bryce Canyon will be appreciated.