Europeans do that trip all the time. But you will want to fly into LasVegas Nevada, not Denver. LasVegas has plenty of RV rentals. You will want to rent that 20 footer. It actually measures 19 feet. It is perfect for a couple who can handle the upper bunk.
As far as where to go, that is one of my most favorite parts of the USA.
- Canyonlands National Park (rent a 4x4 Jeep in Moab and drive into the canyon for the day)
- Arches National Park (see every arch that time permits (hike the loop trail at the far end, and NEVER miss Delicate Arch)
- Zion National Park (hike to Angel's Landing and also in the water through the narrows)
- Bryce Canyon National Park (a 2 to 4 hour hike in the canyon is awesome)
- Grand Canyon National Park (what can I say?)
- Escalante Grand Staircase National Monument (hike to hoodoos and in water-cut canyons)
- Capital Reef National Monument (a beautiful drive-thru)
I see you also mentioned other national parks and monuments. We have been to all of them and they are all worth seeing. 5 weeks is going to be enough time to see everything you want as long as you don't get lazy and burn away days relaxing excessively.
There is at least one visitor center in each national park and monument. Be sure to stop in and talk to park rangers for recommended trails and a free trail guide, and weather forecasts. Spring time can bring spring rains, and rain can bring flash flooding. Just be mindful, not paranoid.