2016 F-150 Towing Capacity

I originally posted this in the general discussion forum, but was referred to this forum for further discussion.

I recently bought a 2016 F-150 Supercrew XLT Sport 5.0L 3.31 axle ratio with 7000# GVWR towing package. I am looking to purchase a travel trailer for camping with a family of 5, but I am getting a little confused by all of the different towing specs. Looks max capacity fully loaded is just over 7,000lbs. (based on using max vehicle load from sticker on door, deducting all weight and dividing by 13%).

I had a 2011 F-250 6.7L diesel and had a good idea of its towing capability, but I traded it in on the new F-150 and am a little confused on the capabilities?
I have been told not to pay attention to the towing charts, so I could use some suggestions on travel trailers or weight capacities for these newer F-150’s.

I am assuming I need to go with a “lightweight” trailer while keeping the GVWR under 5,000lbs as general rule? Don’t pay attention to “dry weight”, correct? We will need a bunk house and they get pretty heavy, so any input or suggestions would be greatly appreciated.

Thank you!