Be very careful with towing at or near capacity.
https://www.ramtrucks.com/content/dam/fca-brands/na/ramtrucks/en_us/towing/2018 Ram 3500.pdf
You must consider several items, to be safe, and legal.
Even though your trucks towing capacity maximum trailer weight is 15620, on paper, you must consider your GCWR (truck, fuel, cargo, people, and trailer loaded).
Refer to the chart at the link above, and then do some math to figure out your prospective weights.
- Your truck is 6810 base weight without fuel
- gasoline is about 8lbs/gal (240lbs for 30 gals)
- average driver weight is 200lbs (add accordingly for actual and passengers)
- cargo weight in the truck is ??
- tongue weight is likely to be 2500-3000lbs as others have noted
- trailer weight - dry vs loaded - having had several RV’s in the past, folks are very accurate with previous comments - dry weight might be 11500-13500 on a 15000 lb max weight trailer - refer to the tag on the rig then take that with a grain of salt, as some manufacturers really fudge with these numbers - I know for a fact.....the only way to really know is to have the RV weighed.....
The really important number is the rig overall GCWR - take all the loaded weights for your situation and add em up - your limit is 22900 lbs.
So, for example, your truck weighs 6810, you weigh 200, full tank of 30 gals of gas is 240, you are already down to a max remaining weight of 15650 for the loaded trailer AND any cargo in the truck.....
You also must consider your states laws - for NY for example, I believe the standard drivers license legally can tow up to a GCWR of 25000 or 26000 lbs, BUT, every state is different.
CA for example, if the trailer GVWR is above 15000 lbs, a driver must have a either a class A non-commercial license, or, a commercial license.
Don’t get caught driving out of your drivers license class - you won’t like the ticket $$$, AND, if you are an accident, you likely would NOT be covered.....
Also, size up on the 5th wheel hitch - if you plan on a rig that has a GW of 15000 lbs, get a 20, 22, or 25k hitch.
On paper, you are fairly close to the maximum towing capacity, and possibly over, without having your exact specifics.
Can your truck do it? Yes, I personally think it will, but, that also depends on your driving while towing.
If you are in a lot of hill country, your fuel mileage will be awful, and you might be really hard on the transmissions life span.
These are the exact reasons I personally went from a 1500 (ate a transmission towing way too much in the hills), to a 2500 quad cab long bed CTD, finally to a 3500 quad cab long bed dually.....the most extreme case I personally saw was a 2500 crew cab 4x4 short bed CTD towing a really really heavy 38ft 5th wheel - he weighed his rig at a truck stop on the way out to the desert camping trip - his rig was almost 6000 lbs over legal GVWR (the 5th wheel was loaded at about 20000 lbs itself)......
Be careful - towing safely, and being able to stop safely in an emergency are the most important things.