GVWR for the 2022 model shows a GVWR of 11,250lb. So figure a pin weight of around 2300-2800lb (20-25%) once loaded. The "empty" hitch weight is irrelevant as you won't tow empty and most of the cargo space in 5ers sits towards the front where a big percentage turns into pin weight.
Your truck should have plenty of grunt to pull but the limitation with 5ers is usually truck payload. The pin weight counts against payload as does the weight of passengers, hitch, running boards, and anything in the truck bed. You also should keep an eye on the RAWR (Rear Axle Weight Rating), again, probably Ok but the entire hitch weight will be on the rear axle with a 5er.
As long as you keep an eye on weights loaded in the truck, it looks viable but you could be pushing up towards the limits.
As far as towing, 5ers are typically great. The higher the hitch weight percentage, the better a trailer tows (semis are up around 50%). In addition, the hitch weight on a 5er sits directly over the axle limiting the leverage the trailer can exert on the truck. Of course, if the truck is overloaded, that can still result in an uncomfortable, possibly unsafe ride.
That said, there is no reason a properly loaded travel trailer (aka: bumper pull) should be difficult to tow. Most of the time wen there are problems, it's too light of a hitch weight (12-15% is good goal, under 10% is likely to develop sway problems).
Tammy & Mike
Ford F250 V10
2021 Gray Wolf
Gemini Catamaran 34'
Full Time spliting time between boat and RV