Greetings,
We have a similar layout of trailer. It's a Zinger 27BH and has a dry weight around 6,300 lbs but loaded for camping we are getting close to GVWR of 7,700 lbs. I tow it with our family Tahoe that has a "tow limit" of 5,500 lbs as you phrased it.
Sitting on the cusp of 170,000 miles on this fantastic vehicle.
Added a few things to make the Tahoe tow a lot better. I added a big transmission cooler and usually see transmission temps around 180 degrees while towing.
I also added some big heavy LT tires to the Tahoe as the factory tires were more for passenger comfort instead of pulling.
I use the Tekonsha Voyage brake controller model that I have had on my last three tow vehicles over the last 13 years. Works great.
My Tahoe is a 6-speed auto and has the 3.08 gear which supposedly is not "ideal" for towing but I haven't really noticed any need to upgrade it as of yet.
I use a standard run of the mill weight distribution hitch with tapered spring bars that is really dialed in, and I have two friction sway bars.
I drive pretty slowly while towing and have a personal speed limit at about 62 mph. That is a personal limit and when I had my dually I drove the same speed.
The rig is solid and tows well and there is not a single time I felt underpowered. However, I would be lying to say that I can't feel it back there. Of course I can.
Oh, I am under all my weights except the tow rating. Pay attention to your set up and watch your temps, drive sensibly, balance your load, enjoy the ride.
thanks!
Jeremiah