I have a 98 Ford like your truck. I also didn't have a factory towing package. I went with a frame mounted hitch. I think you will be much happer with it. I also installed a transmission oil cooler and Hellwig helper springs. 5000lb is a fairly heavy load, I would highly recommend a tranny cooler. They are not very expensive and will may save a big bill later.
Go with the frame mount hitch. You'll have a longer turning radius and youll not have as much bouncing. There alot easier to back to and you wont mess up your tag. its a lot safer to mount with a hitch too.
I gotta say go with the frame hitch. A good class III hitch will give you much better peace of mind when towing a heavy load (5000# is a pretty hefty pull). There's also less chance of marring your bumper. Depending on how high your suspension is, the frame hitch will help level your trailer tongue as well. That will also maker it pull easier and safer.
My dealer recommended a shop, and when I called them they have a class 4 hitch good for 10 000 pounds. Their price is as good as any I have seen for 5000 pound hitches, and since my car trailer will be around 5400, I am thinking it's best to get the higher rated one.
.....First you don't need a 10,000 lb. rated hitch for an F150.
.....Your truck is not rated to tow that much as a 'towed load'.
.....Second the bumper is only rated for 600 lb max load.
.....A high trailer weight can exceed that load on normal dynamic basis while towing from just the momentary weight transfers while driving.
.....The trailer will have electric brakes so you will need a controller in the cab to operate the trailer brakes and a 7 pin power connector back at the hitch.
.....The trailer must have a battery to operate the trailer brakes in event the trailer comes loose of the truck and safety chains.
.....In your owner manual page 137 shows your model and towing capacity for both rear axles, one of which you have.
.....The total gross combined weight for each is shown in parentheses.
.....This GCWR must not be exceeded.
.....I'm sorry but you got a lot of guessing about towing and equipping.
.....It's not something to be taken lightly.
.....The max loaded towed weight is the Gross Combined Weight Rating minus the trucks weight. Do not just go by a trailer weight alone.
.....For example if the trailer weight were 8000 lbs loaded; 12,700 minus 8000
= 4700 lbs for the truck's weight. Very close to max all around if any load was carried in the box you might be overloaded.
...Then there is tire capacity, proper air pressure, transmission cooling etc.
...Just thought you ought to know about all this seeing as you have no experience from the way you posted for help.
It's a safety and liability factor for both you and others while towing.
My position is the age of the post has no meaning.
If some one brought it up, they needed to know.
It is not about a trouble with a truck.
The same type issue comes up over and over from owners that don't know there are parameters and limits to safe legal towing.
This thread will come up on internet searches and should be of value.
The old thread questions are the back ground for the answers given no matter when it is found and viewed..