I towed a 19' hybrid with an '03 V6. The tt weighed in at 3800lbs loaded. The 4Runner handled the weight fine but struggled with the frontal drag and headwinds. The problem was not in the power, the 4 speed trans wasn't suited well. Your '05 should have the 5 speed which would be better. I think you will find it still struggling with a 5000lbs tt. The TTs you are looking at will approach that weight.
I eventually upgraded to an '04 V8 which pulled the hybrid like it wasn't even there. I upgraded to a 26' bunk house at 5500lbs which it pulled well too. Sway did become a bit of an issue at that length though, even with my Hensley hitch.
I'd suggest you keep it under 21' and 4500lbs and you'll be quite happy. As the others said, you'll need to upgrade the receiver, the one on the V6 is not rated for use with a WD hitch. Curt makes a nice one that is bolt on in 10 minutes for about $150. The hardest part is getting the old one off without removing the bumper cover. Consider upgrading the tires if they are the stock type P rated ones. Side walls are too soft and lead to a squirrelly ride.