I vaguely recall one manufacturer making a camper specifically for the 5.5' bed, but can't remember exactly who off the top of my head. Being a niche product in a niche market of a niche market, and a fairly recent development, I'd imagine finding a used one is like finding a needle in a haystack.
That said, I did see an 8' camper in the bed of an F150 SuperCrew roll by recently. They were using the tailgate to hold up the rear of the camper, and in the brief moment I saw them, it did not appear that they were having any issues. I guess you could go ahead and do that but you really should educate yourself first.
The camper could not possibly weigh less than 2000lbs, which is 500-800lbs over the truck's passenger and payload rating. Definitely beyond the stock tire rating. I could not tell if this rig was using LT rated tires or any suspension modifications, but there is no doubt you'd need both.
The camper's center of gravity is much farther behind the rear axle than would be acceptable under normal circumstances. 8' campers tend to be around the 48" mark, and the rear axles on 5.5' bed trucks tend to be near the front of the bed. This can cause handling issues due to the weight transferred off the front wheels.
You really should be sure that you can accept and deal with any shortcomings before you spend large amounts of money. Once you've made the decision and the money has changed hands, it's very expensive to make changes.