Lots of folks will have data for you. I went through the whole 5er learning experience recently so Ill give you my take on it...
What is the pin weight on the trailer empty? If you don't know, its usually inside a cabinet door in the kitchen or you can get it on the website of the manufacturer.
Is the trailer being towed empty or full? Propane full, luggage, equipment, water?
The reason I ask is the truck rear axle weight is a potential concern. While most of us feel that the axle is very conservatively rated at 4150 pounds, you still dont want to exceed it by much if at all to be safe.
I tow a Jayco 31.5 FBHS with about 1500 pound "empty trailer" pin weight. The trailer is like 8400 pounds empty and is rated to over 10,000 pounds gross.
I towed it
without bags first and while it towed nice...plenty of power and braking (make certain to have a nice brake controller...I have a prodigy tuned to about 8V output max), it was too much load for the stock springs...leaving my axle about 1.5" from the bumper stops on the frame. Sure enough, when I hit a bump (wo bags) I bottomed out...setting up a dangerous "humping" bumping ride down the HW. Very very bad stuff.
I then installed Firestone Ride Rite air bags model 2445 I think. And tried again...HUGE difference. Suddenly the truck drives like nothing is attached to it. Each pound of air in the bags picks up 32 pounds of load and transfers it to the axle (so load does not go through leaf springs)...I put 30 psi in mine so I took about 900 pounds of load on the bags, leaving 600 pounds for the leaf springs. Wow that worked nice. The bags can be bought on line for about 260$ , no tax, and ship free. They are easy to install (at least on a 2007/2008 Tundra). I watched the guy do it and I should have done myself...no holes to drill and everything very very well made and fits the tundra like a glove. I attached some pics for you. I paid 495$ installed.
Back to the axle...the bags will fix your ride, but you still dont want to blow the axle rating too bad. Thats why we need your pin weight. Also, you may want the RV dealer to do some work on your trailer setup. The pin can be dropped...allowing more clearance from the top rail of your truck bed to the bottom front of the trailer. I dropped my pin all the way...pics attached. Then the trailer axle had to be raised to keep the trailer level. Only took the RV guy about an hr or
Tundra_trailer weights.pdf, one weight is my truck w no trailer...the other weight is my truck w trailer. You can see that my rear axle w trailer attached is right around 4100 pounds...so I am at the edge...
However...I must say that it tows very nice and stable and stops very easily. Personally, I would tow my trailer that far but would be careful not to add any pin wieght or truck weight...no extra passengers, no water in trailer, no equipment...
Next check your tire ratings...and make sure they are filled to max recommended pressure. Mine are rated at 2600 pounds at 44 psi...and since I am at 4100 pounds I seem to be ok (4100/5200=78% rated load).
Anyhow...these are my thoughts...I also have a tire repair kit and compressor and trailer jack on board. If I do blow a tire, I plan to jack up, fix the puncture on the spot, and refill w air!
Hope this helps...