5th Wheel For Dodge 1500 Hemi 4-Door?
Yes, it is possible, with limitations.
Limitation 1) Weight. Your truck has a maximum gross weight, a maximum rear axel weight and a maximum combined weight (truck and trailer). Most of the trailers out there will cause you to exceed 1 or more of these limits, which is unsafe and unduely wearing on the truck. Furthermore, even if you are within the weight rating of your truck, small gas engines are not very good for pulling heavy weights up hills at highway speeds. In general, you will want to limit yourself to trailers whose gross weight is under 6000 pounds and dry weight under 4500 pounds. There is also some concern about mismatch in truck wheelbase and trailer length leading to poor handling and/or ride, but with the trailers you can pull weight wise (25' or less) this may not be a problem.
Limitation 2) Turning angle. With a short bed truck and a wide trailer, a sharp turn can cause the trailer to run into the cab of the truck, to the detriment of both. There are ways to overcome or reduce this, though. One is to get an extended pin box (one where the king pin is forward of the front of the trailer. This is simple and cheap, but only reduces the problem. You could get a narrower trailer, but that often will not be satisfactory due to lack of space. The last, as you mention, is a sliding hitch. Most 5th wheel hitches can be converted to a 'slider'.
These are often cheap (about $100 more), but a pain to use. To use it, you need to stop the truck, throw the lever, move the truck forward, stop, lock the lever, make your turn, stop, throw the lever, back up the truck and lock the lever. On the other hand, there is at least one gear driven hitch, but the price is pretty steep. One final option is the PullRite Superglide, which automatically slides as the angle of turn gets bigger. Price is in the middle.
If you can get an 'under bed' mount for your hitch, you may prefer it. Even those little REESE rails left in the bed when the hitch is removed annoy me. The under bed hitches claim nothing left in the bed (except the holes the hitch attaches through).
The truck needs to be set up for towing, particularly with a transmission cooler and preferably a trans temp guage. High rear end gear ratio will help with towing, but hurt gas milage. Plan on slowing way down going up hills.