Two things to check: Max recommended towing weight in owner's manual, and weight on individual axles, especially the truck rear axle. Beware of published curb weight specs. They aren't as grossly understated as they used to be, but they are often low, especially if the fiver has optional equipment (icemaker, generator, extra TVs, etc.) We tow a 33' fiver that has a loaded weight per a truck scale of 13,000#; pin weight is just under 3000#., Ours does have a generator in the front compartment, which adds about 250#. Our max towing capacity per owner's manual is 14,000#; we are a bit over the GVWR for the fiver. The comment about holding your better half to 1500# of gear and watching the weight in your water, propane and holding tanks is right on. In adddition to max towing weight and trailer GVWR, you are likely to be close to the rear axle GAWR; we're about 1000# under. Again, a truck scale is the only accurate way to find out. If you weigh both truck axles with the fiver unhitched, then hitch up and weigh first the truck, then just the fiver axles, a little math will give you total weight for the fiver and the weight on your rear axle.
This does load the rear axle pretty heavily. You want to make sure you carry the right tire pressure and watch tire, rear axle, and bearing temps, especially in hot weather. If you are running over 60 mph in 95 degree plus weather, you will find rear tires running at 175 degrees or more and the rear axle (differential) to be as much as 180 degrees. My dealer recommends a transmission flush and changing all the gearboxes every 30,000 miles. Only problem we have ever had is that the rear tires both suffered tread separation after about 10,000 miles of towing. At the time, temperature wasn't that hot--about 75 degrees. We think the tires were defective. An infrared pyrometer ($35 or so at Sears or any well-stocked tool/hardware store) is a great investment. We got one after the rear tires went out; the tire shop shot the rear axle and tires when trying to see what might have gone wrong. Use it to check tire & bearing temps at every stop. It will help you find a leaky tire or bearing running hot.
One other tip. Run tires with the least aggressive tread you can find. They will run cooler.