The 264 would be too much for your truck IMO. A brief google search turned up a max tow capacity of 6,200; but it may vary with engine and rear axle ratio. That dry weight is misleading. Option packages will add a good 500 pounds. Then add liquids; e.g. fresh water and maybe some grey and black from time to time; 8lb/gallon approximately. Then add your food, gear, kitchen supplies, etc. and you will be well into 5,000+ territory.
2012 F150 FX4 Ecoboost, 2016 Surveyor 274BHS
2003 Yamaha FJR1300, Demco Premiere Slider
1969 John Deere 1020, 1940 Ford 9N, 1948 Ford 8N
Jonsered 535, Can of WD-40, Duct Tape
Red Green coffee mugs