The important factor is your brakes. That's why at least most late 1980s and later model Toyota trucks have really heavy duty twin piston brakes up front. Not sure about your model though. That's a major factor that guides tow ratings.

GVWR is only for the truck itself, as I understand it. It doesn't include what you tow. The tow rating you need to concerned about is your combined gross/towing weight (GCWR I believe) On the 1989 and later Toyota trucks it's 7800lbs. It's probably a little less on your truck, but 5800lbs sound safe to me.

But be sure to double check those brakes. Especially if you anticipate any long down grades on your trip.