Well, it won’t pull like your Cummins but it will get you there. I have a 2001 F150 5.4 4x4 with a 3:55 axle. My TT is 16’ and only 3000# loaded and it’s a piece of cake to pull. I stayed small and light because most of my travel is in the mountains. OVERALL, I get 14mpg towing, the same as solo town driving. I don’t like high rpm climbs and don’t think I’ve ever seen 4000 rpm but out of curiosity I’m paying closer attention now.
You’re probably a good 5000# and you’ll notice that weight climbing grades. My guess is you’ll be in 2nd gear and probably over 4000 rpm in those conditions. But the engine will handle that rpm just fine. Again I’d guess your mileage in those conditions probably in the 10 mpg area. But guesses not being very useful you could do a search along the line of F150 and gas mileage and find a lot of posts, it’s a frequent topic. And many posters may chime in with their own experience. But I don’t think you’ll be disappointed with an F150 for that job.