Man there's a lot of doomsday posters up above. There's no need to have to go out and buy a different tow vehicle. There are campers that you can tow, although they will be on the smaller side. First of all, I would rule out a 5th wheel, unless you are talking about one of those tiny ones that are about 30 yrs old or older.
While doing your homework, you and your wife need to decide what you in want in a camper. The amenities, the size and etc. then see if ere is a camper out there that meets those needs that can be towed with your truck. Then you will need to decide whether or not you are willing to change your tow vehicle if you can't find a trailer that you can pull right now.
There are trailers out there that you can pull, you will just be limited to what you can pull. Given the numbers you gave, I would definitely stick to a camper with a gwr (wet weight) of less than 5200lbs. You don't have to get one that heavy. You can always go smaller.