Hi csharp, welcome to the forum!
I have an '05 3.7 and pull a 19' travel trailer, dry weight is 2700 lbs. I also estimated around 1000 lbs for cargo and tried to travel with all tanks empty.
I would definitely not want anything any heavier.
We did about 3500 miles two summers ago, from Toronto to Cape Cod then up the coast, through New Brunswick to Nova Scotia and back to Toronto through Quebec.
There were some significant hills along the way, and she often struggled to maintain a decent speed. A few big hills in Maine I started losing speed and had to put the hazards on and let a couple of transport trucks pass me, but most were OK.
It's easy to get carried away with that 5000 lb number - I made the mistake of telling my wife that was the max, so she was shopping for 4900 lb, 25' trailers
I put my foot down (haha) and said our limit was 20' and 3000 lbs.
The other thing I would say is a necessity is anti-sway and weight distribution hitch setup. I pulled the trailer home just on the ball in some decent crosswinds and it was scary, no way was I going to be comfortable for 3500 miles like that. I had a Reese system put on and have been very happy with it, it really ties the Jeep and trailer together as a unit and makes it much more pleasant to drive, even in high winds.
Other things - extra transmission cooling would be advisable, turn off overdrive to minimize shifting, and I found that cruise control was helpful in that respect as well.
Oh, and based on my experience, budget for about 11 mpg.
Hope that gives you some insight!