I have an older F150 that has similar weight ratings.. I pull a Jayflight TT, that has 24 ft box, but a total length of 28ft. It has a gross max weight of 7000 and a dry weight of 5200.. I can tell the trailer is there and revs go up a bit on long or very steep hills, but not dangerously so. I do have a couple of suggestions as you look.
Be sure you look at the actual stickers on any trailers you like. I found sometimes there is a BIG difference between the published dry weight in sales brochure and what the trailer actually weighs delivered to dealer. That published dry weight often doesn't include any accessories or options.
The other thing is my truck has the P series tires mentioned previously and they do feel a little soft and squishy when towing. After much research, I learned to add about 5-10 pounds to rear tires when towing. (this is above the door sticker recommended rate - but below max on tire). This helped so much, that when I bought new tires, I chose to go back with the same tire. I use my truck as a daily driver and so for the many more days I make that commute to work, I prefer the softer ride. This decision was made after discussion with several tire companies and truck service companies.
