As some mentioned, you might want to figure out if your truck is enabled for "Tow/Haul" mode. It wasn't standard until 2012. That will tell your truck to change its shifting points, use more engine braking, and stay in the sweet spot for maximum torque.
Do you know what your gear ratio is? As others said it will affect tow rating but will also affect your truck's ability to deal with inclines and hills, and whether or not your tranny will be constantly searching for the right gear - i.e. killing your transmission. Generally the shorter gears like the 3.92 are better for towing and taller gears such as the 3.21 and 3.55 are better for fuel mileage. I've got 3.21 gears in my 2015 but it's also got the 8-speed transmission so it's able to handle the loads better than a 6-speed.
I'd say that you'll be fine for shorter, flat trips but will want to investigate things more if your truck is maxing out with this boat. I assume that this boat/trailer will have trailer brakes so you'll need to either have a brake controller in your truck or install and aftermarket one. A 5,000-6,000 pound boat will absolutely 100% push your truck around in an emergency stopping situation.
