Once again on this tow- related thread we're seeing the fact that the US tow ratings are way lower than those across the ocean. It's both good and bad if you ask me..
As far as power goes, the 5.9 can certainly tow a 6-7k+ lbs trailer with no issues. Heck, vehicles with much smaller engines can do that relatively easily. All V8 ZJs here are rated to either 7300lbs or 7600lbs towing capacity; anything over ~1600lbs (750kg -> 1630lbs) will need to have trailer brakes though; either electric control or surge brakes.
The issue with the ZJ is the weak brakes, someone mentioned softish rear coils (true), and tranny cooling capacity is not exactly the best from the factory. Power is not an issue; I was towing a 6500lbs trailer with around 350lbs tongue weight, and my rear tires easily broke loose (242 swap, driving on RWD) on damp pavement on 2nd gear - tires being only two years old and 85% thread. The damn thing didn't even jump out of OD/ TC lockup on mild hills doing 55mph. Outside temp at that time was around 60*F so the tranny temps stayed low, especially 'cause I was mostly on flat land on OD/ torque converter locked up. On hilly terrain 3rd gear is the way to go. I've towed 5-6k lbs numerous times, and it doesn't even feel like it's straining the niner. Having legally towed similar sized trailers on smaller vehicles I can tell you that a ZJ niner is a pretty good tow vehicle, as long as you keep the tongue weight at reasonable levels, have trailer with brakes and don't go over ~60mph (80km/h, or 55mph is the limit here anyways with a trailer).
With the 5500lbs (or 5000lbs?) rating there across the States, keep it the legal level, get a trailer with brakes and do it. I honestly see no issues whatsoever towing that weight, keep it around 60mph though. I know sure as hell a full size pickup is much nicer to use on long trips/ heavier trailer, but if you don't have one, you don't. People tow 5000lbs+ camper trailers or big boats around Europe on vehicles like ZJs or Toyota RAV4s all year long. If it's not an issue here, shouldn't be an issue there either
1998 Grand Cherokee 5.9 LX daily driver, 1.75" BB, 32" KM2s, HPD30 Eaton e-locker/D44a stock LSD, 4.56 gears, custom- fabbed tube bumpers and tube fenders,...
1990 XJ Limited (4-door), 4.0 I6, AW4, NP242, ***rolled and totalled @ 165k miles***
1990 XJ (4-door), 4.0 I6, AW4, NP242, PBR 42" tires, Unimog 404 portal axles, 110" WB, full cage + uniframe completely rebuilt, front 3-link + panhard / double triangulated 4-link rear,... ***SOLD***