Two reasonable possibilities above, tires and inadequate payload, but I'm not sure either would explain this specific symptom, i.e. a side-to-side sway that goes away when he backs off the go-peddle. If it were a travel trailer, I would suspect insufficient tongue weight. That's unusual in a 5W, but it could be excessive weight behind the trailer axle, such that the balance is off and the trailer begins to sway. That sort of trailer sway goes away as the truck slows because trailer weight/balance transfers forward when decelerating.
ogstoner1: Is this an all the time thing or just once in awhile? What speed? Is the trailer obviously oscillating, pushing the truck around?
My first action would be a trip to the scale with the truck & trailer loaded as usual for travel. Get truck & trailer weights, hitched and unhitched, with separate weights for both truck axles and the trailer axle weight as a pair. That will let you the trailer derive pin weight too.
