We, too, tow our 34' Limited with a 2005 F150 Supercrew Lariat. It has the factory installed tow package and I have been very satisfied with its performance in towing.
Something that hasn't been mentioned is the actual weight of 34s. OP said he was getting the trailer for $7500 so I am guessing it is an 80s model.
1984 34' Sov. - 6950# dry
1988 34' Ltd. - 7025# dry (this is us--well below the truck's max towing abilities)
1993 34' Ltd. - 7100# dry
1997 34' Ltd. - 7950# dry
We get the question at campgrounds often "You pull that big thing with just an F150?"
The answer is "Yes, it is a long trailer but relatively lightweight and pulls like a dream."
Easily distracted by shiny objects.