2004 Ford Ranger 4.0L V6 4WD Automatic

I don't have experience with that exact truck, but I used to tow with a 1997 Aerostar with the 4.0 OHV V6 that had a little less power than your 4.0 SOHC. With 3.55 gears and the little 205/R14 tires it did fine pulling a 4400 GVWR hard sided ultralite. It would pull Cascade passes at 45-50 and got about 12 mpg towing. Power-wise it did almost as well as a 4.6 V8 Expedition but got much better mpg. So, for towing about 4K that Ranger would be ok but 5,800 would be pushing it. You would be over 10K combined with 200 hp and IIRC 250 torque. Modern gas pickups are roughly double that and will move 20K combined, but they are working hard in the hills.

There's was a guy who used to pull a small 5er with the same model.

Seems unlikely a truck this old, small and underpowered would be fun to drive with TT. And while I believe you about the alleged 5,800 pound tow capacity, I DON'T believe Ford