Yep... I tow a #5000 GVWR TT with the truck in my sig and I know it's there on the grades...
I have a truck that has a "tow rating" of over #11,000 too... So there you go..
It's just what works for me.. I know I can tow more, but I choose to tow what I tow because I've been towing for a long time now, and have "been there and done that" so there you go.. :)
Do whatever you need to do of course... But only you know if you like to be pedal to the floor and screaming rpms and going maybe 40 mph...
Don't have any clue if that's what you will see, but I've done that and it ain't fun... :)
Good luck!
Mitch