My F150 has #7700 GVWR, but only #4050 rear GAWR.. Towed the same #5000 TT with a 97 F150 with only #6250 GVWR and #3200 rear GAWR...
Needless to say, I was over on both, but towed it for about 12 years and never a problem.
Right, wrong, whatever.. It was my choice to do it I felt comfortable and enjoyed the tow and never felt unsafe.
Current truck tows the trailer even better and I can tell a difference, but it's mostly the power of the new truck compared to the old one.. Not so much the handling. That's not much different at all.
Anyway, it's all up to you what you do.. Someone else on this site keeps posting questions asking what they should get and we've all posted our opinions, but it just keeps going round and round.. ;)
Good luck with whatever you decide! :)
Mitch
