OP just needs to look at the door stickers to determine the payload and the axle in the TV.
If indeed it is equipped with the payload package and has a 3.73 rear end that truck should be rated to tow 11,300. Should have a 157" WB.
We upgraded from a Suburban with a tow rating of 7,800 to an F150 rated at 9,500. We have a 26BH that comes in about 6,600 packed for travel. The F150 is a huge improvement over the Burb.
With the Burb I could tell the difference between a full tank and a half tank. We were right on the rear axle max. I had to watch for passing vehicles and get to the far right of the lane to minimize sway.
With the F150 I can run up to 10mph faster with no issues and the sway from passing vehicles is almost non existent.
I have had 250's and 350's in the past and yes they tow great. For me the F150 is a daily driver the tows the camper and the boat. It does both great.
A Smart phone is one that is NOT in your hand while driving!