I did for 10 years what you are contemplating: I towed a 30' TT with dry weight of 5333 lbs with a 1/2 ton 5.7L 2003 F-150. Probably around 7000 lbs when loaded for trips. After our last "long" trip I came home ready to sell the TT and retire from Camping. The next spring (2 years ago) I traded the 1/2 ton for my 3/4 ton diesel. Last spring traded the old TT for a heavier one (both in my signature). My philosophy now is, "It's way better to be over powered than underpowered."
My advice: either get a smaller TT or a beefier TV.