Unless something drastically changed between the 2005, and the current models, it should do just fine.
I had a 2005 Nissan Xterra. Same engine/transmission/drivetrain, as the longer Frontier.
I towed our current travel trailer with it for 5 years before trading for the F150. The Nissan had 90K miles on it, ran great, no issues.
It had plenty of power towing our 25' TT. It is 3995 lbs empty with the options. I loaded it lightly, and kept the waste tanks empty when traveling. Kept maybe 10 gallons of water onboard.
My F150 is bigger, with a 5.4L V8, and I don't think it would outrun the Xterra while towing by much of a margin. 4.0L, 265 HP, 284 lb.-ft. of torque, vs. 5.4L 3V V8, which develops 310 hp and 365 lb.-ft. of torque. The F150 is much heavier, so the added 26 HP, and 81 lb.-ft. of torque, go towards carrying the extra weight of the truck, not necessarily the payload.
I'm in FL, and towed all year. Engine and transmission stayed cool. When I changed the transmission fluid, it was still a pretty color, no burnt smell. But when towing, I change the tranny fluid once a year. 90K miles, I couldn't find any flaws. I only traded to get more room for hauling 'stuff'.