Good truck for towing

Short answer, depends.
Long answer, depends.
Model year of truck, important
How truck is geared, important
Miles you plan on towing while FT, important
Your experience towing and willingness to mod the truck suspensions, important
Extra short answer, most all 5.7 Hemi half tons From the last 15 years will handle that trailer. Anything ‘14-up with the 8 speed and 3.92s will “pull” the same or better than any 2500 with a 5.7.
Any 2500 will “handle” the trailer better.

Possibly make it work if you carefully watch every pound and don't pack heavy: 1500.
Comfortable: 2500

The 2500 is best choice for that size. Why limit yourself to Ram 5.7, when there are also good gas engines from the other brands.

Jerry

Whatever you buy watch the payload. Ram's are notorious for having extremely light payload as the crew cab and 4 X 4 add a lot of weight. I'm guessing your 5,600# dry weight trailer will have a GVWR of around at least 7,000# and you will likely load to close to that.

If so you will have a proper tongue weight {13 percent} of 910# + another 100# for the weight distribution hitch which comes to 1000+# before you load anyone or any thing into the truck. A 1500 will do it depending on where you travel but it will need at least 1500# of payload and I have seen some Ram 1500's with less than 1,000.

Keep in mind that 30' of TT is a lot to ask of a half ton truck when the wind blows and/or in the mountains. Good luck.

:C

Even better, find a used 2500 diesel

You will never tow dry weight. Add the batteries, propane and all the goodies and you could be 7500#. Also the length. Be safe. That is my $0.02 worth...
Get a 2500/250...

Loaded and wet, 7000 pounds. Tongue weight 900 pounds plus hitch. Could be ok with the right 1500. What will you carry in the truck?

Have you used the search function on the forum? This question has been asked and answered hundreds of times - if not more.

One ton diesel is best.
Three quarter ton diesel is next best.