#3700 DRY TT will weigh #5000 or more when loaded up.. Big question is what is the TT GVWR?? Yes, you might not load it up to it's GVWR, but I sure did on mine.. :)
It's DRY weight was around #3400 and it weighs every bit of it's #5000 GVWR when loaded for game.. :)
I towed it with a 97 F150 that had a tow rating of #7700 and it worked pretty good to tow it.. It was a decent tow and I did it for over 12 years and it had a 5.4 V8 in it...
Anyway, I tow the same trailer with my 2013 F150 Ecoboost and it's like I'm not towing anything really... :)
Anyway, DRY weights and what you actually load in it are going to be different, so keep that in mind too..
Good luck!
Mitch