Well...My 13 F150 has a "tow limit" as you put it, of #11,000.. It's a Ecoboost with the MaxTow package. I have payload sticker that says it's good for up to #1900 of extra stuff in the truck, including the tongue weight of the trailer.
I'm towing a #7000 GVWR 26' TT and I'm pretty much maxed out on my payload and I know I'm pretty much maxed out on the trailer too.. I pack heavy and know it!
It does fine thanks to the turbos, but the truck itself is basically at it's limit for my own comfort level and how I like to tow..
Don't get me wrong.. It tows great and I love towing this TT with it. Half the fun of the trip is the getting there part as far as I'm concerned!
Anyway, if you get your hitch setup and dialed in, you should be fine. Power won't really be an issue for you, but you will have to let the 5.0 rev some to get into it's peak power range.
I've done some additional mods to the tires, brakes and suspension over OEM to just help my towing experience, so there's that too..
Good luck and just work thru the hitch setup and loading of the truck and trailer and you'll be fine.. Mitch