Hi halfdozmom -
Some things you need to know about the individual parks:
Zion:
You will not be allowed to drive your own vehicle through Zion Canyon. Except for the rare instances where a visitor cannot ride them due to specific medical reasons, visitors must use the free, wheelchair-accessible shuttle buses. The buses make multiple stops at scenic points around the canyon so do a little reading about them. As well, parking lots can fill early and quickly. There is a grill and restaurant but I'd bring your lunch along. This is a VERY busy park.
https://www.nps.gov/zion/index.htm
https://www.nps.gov/zion/planyourvisit/zion-canyon-shuttle-system.htm
Bryce:
There is a shuttle but you can also drive your own car to overlook parking lots at this park. Some of the viewing points are quite a number of steps away from the lots. There is a rim walk that is paved and mostly level; you do need to be able to walk to it from a parking area. They have handicapped parking spaces at overlook lots...which can be very busy. There is a seasonal dining room at the lodge, pizzaria and general store.
https://www.nps.gov/brca/index.htm
https://www.nps.gov/brca/planyourvisit/accessibility.htm
Capitol Reef:
Your dad will enjoy the scenic drive! Lots of to be seen from behind the windshield and short stops:
https://www.nps.gov/care/planyourvisit/scenicdrive.htm
You all might enjoy a 'lil visit to Gifford Homestead too, Be sure and try to buy a little fruit pie or two made from the pioneer orchards; they sell out fast! There's no other real food in the park so pack a picnic or grab something in Torrey.
https://www.nps.gov/care/learn/historyculture/giffordhomestead.htm
He might be able to handle a stroll on a boardwalk to see the petroglyphs?
https://www.nps.gov/care/learn/historyculture/fremont-culture-petroglyphs.htm
Arches:
You're going to need advance, timed-entry reservations for this one unless entering before 7:00 AM or after 4:00 PM, and most of the arches are not visible from the road/parking areas. Still, you'll be able to see some impressive scenery; this website might be useful:
https://www.moabadventurecenter.com/arches-national-park/driving#:~:text=Take%20a%20quick%20detour%20to,South%20Window%2C%20and%20Double%20Arch.
I'll caution you NOT to just stop in the middle of the road to take it the views, though; a good way to get rear-ended or annoy others on a mission to get to popular trailheads. Pull over to designated viewing areas. No food in the park; pack lunch in a cooler.
Also:
https://home.nps.gov/arch/planyourvisit/timed-entry-pilot.htm
https://home.nps.gov/arch/planyourvisit/physical-mobility.htm
Canyonlands:
The closest unit to Moab - and the only one your dad would be able to manage a bit of - is Island In the Sky, some 32 miles out of town.
https://www.nps.gov/cany/planyourvisit/islandinthesky.htm
You can drive the road in your own vehicle, and there are a few accessible viewpoints. No food; pack a cooler picnic.
https://www.nps.gov/cany/planyourvisit/physical-mobility.htm
Accommodations: if you haven't made them yet, you need to do that right away as they fill quickly for the season! I'll agree with the comment above that trying to do all 5 in 5 days is going to involve a lot of time in the car.
Hope this helps!