Unfortunately, your F150 probably won't do too well with that rig. The top max tow rating for your rig is 8000# for a supercrew 4x2 V8 5.0l with a 3.55 axle ratio. GCWR is 13,500. Base curb weight is 4664#'s, max payload 2130#'s, max pin weight 1130#'s.
The hitch's capacity has little to do with your trucks towing capability, but you would be over the hitches max rating by 100#'s and you haven't loading anything into the trailer yet.
So.. dry pin weight.. you're over by 30#'s already, trailer dry weight.. you're over 130#'s already, GCWR you are in the black, but only by 700#'s, max payload you're in the black there too with 975#'s, but you can't exceed 700#'s to stay within the GCWR.
Basically what that means is you have 700#'s to play with to stay under GCWR. That would be passengers, cargo, water, weight distribution hitch, trailer batteries, food, clothing, kitchen goodies, etc etc etc. Just ballparking it, it's pretty common to use a figure of 1000-1500#'s above dry weight of your trailer for just the basics, so it would be extremely difficult to stay under 700#'s anyway, but it's kind of a moot point since without adding a single thing to your trailer or tow vehicle (passengers included) you're already over the max rated allowances on your pin, and tow capacity.
I fear your dealer may have steered you wrong.