actually no- "gross trailer weight rating (GTWR) is the total mass of a road trailer that is loaded to capacity, including the weight of the trailer itself, plus fluids, and cargo, that a vehicle is rated to tow by the manufacturer." loaded with everything it can carry max weight.
According to Airstream
all 73 Sovereigns weigh just under 5000 lbs.
What engine is in your truck? If it doesn't have a factory tow package, you might need a transmission cooler. Try posting about this in the towing area, you might good someone who has a recommendation to improve the truck