I had a 2010 F150 with the 5.4 and 3:55's and had a 24 ft Kodiak that weighed in at about 5200 lbs ready to camp. It pulled it pretty well around the flat lands of Illinois and Wisconsin but I don't know how comfortable I would have been pulling it through the mountains.
Things to check: Does your truck have a trans cooler? Trailer Break Controller? Also, check the sticker on your drivers side door to get an idea of your payload limitations. (I say "idea" because the only way you will know for sure is to have your truck weighed)
Things to consider. I know that I had to be very mindful when loading my trailer and truck because I was within a couple hundred lbs of the payload limit. If I would have added a friend to our trip, I would have been over payload.
If you have the trailer break controller and trans cooler, you should be good to go. Hope you enjoy it.
2016 Nissan Frontier Pro 4x 6 speed manual. (Future TOAD?)
2014 Shadow Cruiser 313 BHS (Sold)