Welcome to the forum. You're right to inquire, as there are a lot of people who know 'their stuff' here.
I'm no expert, but have spent a lot of time listening to and reading info by 'owner experts,' before buying my own camper.
I read about tow capacity/PAYLOAD capacity (just as important) hitch weights and how the numbers stated in the Jayco info about a particular camper are STARTING NUMBERS...in many and most instances, the weights GROW from there.
The weights stated by Jayco for that unit and the numbers for your tow vehicle do not allow you the safe percentages necessary, as a buffer to safely tow.
No. I would not tow that camper with your vehicle. The numbers are maxed out. Not safe. If you had to tow it ONE TIME, no hills, etc etc. I'd say it CAN do it...EMPTY with weight distribution. BUT, towing regularly on trips, up and down hills etc etc. No. I wouldn't do it.
Dealers will tell you anything to sell a unit.
There are lots of unit within the 5,000 GVW mark. Check out some of those. Manufacturers are getting more and more ingenious with their design for small campers. That 5,000 is still coming in tight with your tow statistics, but it'd be much safer.
Start here. This guy does lots of camper reviews and does it well. I like that 169FSX

and that surprisingly light, GeoPro by Rockwood.