The V8 in that 4Runner is a 4.7L, not 5.3.
We also have a 4.7L V8 4Runner, and tow a 21.5' hard sided TT, GVWR is about 4800 lbs. The model is a Rockwood Mini Lite, 2109S, with a slide - you might google it and see if the floorplan might fit your needs. It tows it adequately, but we have some serious long inclines where we go into the mountains, so with regard to my personal comfort level, I wouldn't care to tow anything any heavier with this rig. To me, the largest factor is how steep and long any inclines you tow on are.
My WDH with sway works well, and I have never gotten any sway whatsoever. I changed out the puny OEM trans cooler and installed a larger one to successfully knock the trans temps down. I use a Scan Guage II to monitor trans temps. I tow in the extreme heat of the SouthWest desert.
Yes, you must have a brake controller to tow a trailer that heavy.
Good luck with your decisions!