OP...
I want to clear one little thing up.. Having a hitch on the back of the truck is not all there is to a tow package.
There is also an external transmission cooler, specific gear ratios, possibly special tires, brake controllers, tow haul setting for the transmission, and some other things.
6500 lbs is a moderate load for the RIGHT F150.. for the WRONG F150 its a death sentence.
People get confused with F150's because they all look the same.. but how they are mechanically equipped can make them totally different animals. Some trucks.. like your platinum are nice, plush, rides... with about 800-1100 ish lbs of payload (My 2013 Kia Sorento has More than 1100 lbs of payload, as do most minivans... for example). Without the Max Tow and Max Payload packages these platinums are basically boulevard cruisers or grocery getters (There is nothing wrong with this btw for the use of the truck)
I highly suggest upgrading this nice truck to at least an F150 with the Max Tow package in the XLT or Lariat trim... Those power auto swing out doodads weigh a LOT and as another poster has already alluded to, the more doodads you have on your truck the less cargo it can haul. This is especially true if you want to keep RV'ing.
F150 Max Tow or just about any F250 will make this issue go away and get you on your way to a much more comfortable tow.
I also want to inform you that how much something weighs is only a part of the equation.
Manufacturers have ZERO control over what you are going to hitch to their trucks so they try to give you a safe rating to go by. A 3500 lb flatbed trailer with 4500 lbs of flat steel is going to tow EASIER for your truck than a 4500 lb travel trailer.
Why? Aerodynamics... Pulling a travel trailer is like standing three 8x4ft sheets of plywood on their edges, stacked on top of each other (again on end, 12 ft tall total) and then pulling them down the interstate at 60 mph. That is a HUGE aerodynamic load compared to a low profile trailer.
In my humble opinion... Ram is the only manufacturer who will actually tell you what series of truck you NEED for what kind of trailer you want to pull.
They flat recommend a 3/4 ton or a 1 ton for folks wanting to haul an RV.
Here is a useful page for EVERYONE to check out that Ram offers, it provides a lot of good information for everyone, especially someone who is not familiar with all this towing jargon you are hearing!
before you buyThanks and good luck!
Jeremiah