You need to run the numbers but probably not.
The newer pickups have a higher rating than the older trucks. I own a 2004 and know that in 2005 the numbers started to climb but the new trucks are just built for heavier loads. At least by manufacturers printed material. If you open the drivers door on the truck there should be a sticker which gives the GVWR. Weight your truck with fuel and family ready to go camping and what's left is for carrying the camper.
2005 Ram tow ratingsI don't know what the numbers are for the 5er you looked at. A 5th wheel will have about 20% of it's loaded weight in the bed of the pickup. This is what overloads most pickups in the 5th wheel world. The truck probably has 1,200 to 1,700# of cargo capacity for family, bikes, hitch (200#) whatever else you load in truck and the camper's pin weight (hitch). A 10,000# camper (loaded, not the dry weight) will put 2,000# in the bed. Even at a loaded weight of 8,000# (small in the world of 5ers) a pin weight of 1,600# will exceed your pickup.
Cougar Half-Ton Specifications