There are plenty of sub-5000lbs hybrids out there that you should be able to tow. I also have a 6000lb tow rating and currently tow a X23B that is 4026lbs dry according to the sticker on the trailer, and 4950lbs gross. That's about as big as I'd go, but it's plenty roomy for our family of 6.
2004 Jayco X23b
2005 Nissan Pathfinder LE 4x4