^ Yes, it's the 5.3, and if it has the 3.2 gears, its the 8 speed.
(GM is in this thing now where they have like 5 or 6 engines, 3 trans and 2 different T cases going on in current models, depending on the package)
OP, since you're not experienced at towing and are/will be in mountains unless you don't take it out of your subdivision, it's alot of trailer for that truck. Be careful with your driving techniques, especially on the grades.
That said, that truck will pull that trailer just fine, all day today, tomorrow and 5 years from now. The 8 speed is great for towing and IMO having driven one of them for a couple months (same truck but with a bow tie) and having a 2016 5.3/3.42 6 speed, the new 8 speed makes the 5.3 feel like more than it is, considering it has the least power of the big 3 for the "small" V8s.
Pump the tires up, get the wdh adjusted and have fun camping!
"Likely be OK for short trips on flat terrain, but if it's windy or hilly, you're going to spent a lot of time at 5000 RPM or so, and the trans will be doing a lot of shifting."
This is a true story, other than you can lock out whatever gears you want to, to minimize shifting up n down alot. No different than any naturally aspirated gasser pickup towing a 4-5 ton "wall" down the highway.