br549, first of all, welcome to the Forum. Alot of good suggestions have been given already, hope you don't mind a couple of other thoughts.
When I first purchased my 30SK, I had an '05 F150 SuperCrew. Had the same issues you're experiencing when pulling it home from the dealer. Immediately ordered/installed Firestone air bags on the truck. This prevented the squatting of the TV only. I also had to run 40 psi in my rear tires instead of the recommended 35 psi; this is where I really noticed a difference in the bucking. So here are my thoughts:
1. What tire pressure are you running on your truck? What is the MAX pressure on your door label. This may be a limiting factor in correcting your problem. Remember, too much and too little pressure can damage tires.
2. Is the rear of your TV squatting too much? With the 5er attached, is the TV at least level or nose high/low? Air bags or Timbrens will help.(personal choice here, many arguments as to which is better.
3. Adding water to the fresh water tank will lighten the pin weight of the trailer. Too much of this can cause BAD things to happen...several years ago, saw my best friend almost flip his truck and TT because of too lite of tongue weight. Pin weight should be 15-20% of trailer weight. Usually, a light pin weight aggravates chucking instead of alleviating it.
4. Have you had your TV and 5er weighed on the scales yet? If not, do so. Check weight of each axle. This will tell you how well balanced your setup is. No, I'm not one of those weight police guys, but knowing this will sometimes show us problems that we didn't know we had.
If you can give us answers to some of these questions, someone may be able to give better advice...maybe even the kind that doesn't cost you anything.
As you can see in my sig, I knew I was pushing my 1/2 ton (and I used to bleed FORD Blue!). When I could only maintain 40mph going up the San Jacinto bridge on TX-146, I knew I had too much 5er for the TV. That ain't a problem anymore! LOL.