i would say NO. do not expect a HZJ77 to tow 5000 lbs comfortably.
the 1HZ is nice, the 1HZ-T is nicer, the 1HZ-TI is sweet but not a chance being able to tow 5000 lbs comfortably.
i have made this warning to many in Canada and yet watch them buy the truck and 2 years later sell them and buy NA diesels to do the tow.
it is your money, do what you want. i recommend 3500 lbs MAX to my customers unless it is a "twice a year" move the trailer to the camp ground or the boat to the lake move.
of course once you hear a couple blokes say "sure it will" and you get all horny over the truck, common sense goes out the window.
x2. The 1HZ's one hundred something (30? 40? 60? I can't remember the exact figure) HP will only take you so far.
Better safe than sorry.
Juan