In stock configuration, you're already too high to tow a typical 5ver where it is level and unlikely to damage your bed rails due to limited clearance when traversing driveways and inclines without major mods to raise the 5ver coach body. If you install taller tires then you will aggravate the situation. I was faced with the same problem with my 3500 4x4 (w/ stock tire size) and 33' Hitchhiker. I was looking at raising the coach up to four inches in order to solve this problem, which I really didn't want to do because of raising the center of gravity and the overhead clearance issues of the coach. I found the Mopar part # for the rear lowering kit for my Ram on this forum and ended up lowering the rear of my truck 1 7/8" (removing the aux. leaf springs, installing shorter spacer blocks and U-bolts, and installing the shocks supplied with the kit) which solved my problem without modifying the coach. Now I have more than enough clearance between the bed rails and the nose of the coach and the coach is very close to level when dry and on the hitch. When fully loaded it is just right.
From what I understand, all 5vers are manufactured to have approximately the same hitch pin height when level, unless special ordered to accomodate a higher hitch height, such as in your case (stock height 3500 4x4 or with 35" tires over stock). (The exceptions are the 'toybox' fifth wheels, which are higher due to their applications. ) This raising of the coach is generally done by moving the axles to where the axles are under the springs rather than on top of the springs (often referred to as 'flipping the axles', but that is not a good way to describe the mod) and/or by adding 2x2 or 2x4 steel tubes on the frame where the spring shackles mount and re-mounting the spring shackles. In the case of my Hitchhiker, the axles were already sitting on top of the springs so the only option I had was to weld the steel tubes into place, permanently altering the coach.
IMO, it is really not a good idea to raise the coach beyond moving the axles from above the springs to below the springs, which may still not solve the problems associated with a high hitch height on the truck (as in my case). I am fairly certain that there is a Mopar rear end lowering kit made for your Ram that is specifically for this purpose, a kit very similiar to the one I installed on my '01. It appears you have a choice - have a truck that is suited as a tow vehicle, or have a stock height or raised truck that causes you to have a number of i$$ues when towing a 5ver.
FWIW, I think my truck looks much better with the rear end lowered the 1 7/8", having the 'leveling' effect.