Many 3/4 ton trucks couldn't safely pull a 37 ft 5ver so the answer is no. Look at what your Tundra can pull in your owner's manual weight wise and also the cab configuration ie. crew cab or standard, engine size, transmission type and final drive ratio all come into account. If you have the bigger motor and the manual says you can pull say 9000 lbs you may be able to pull a small 5ver but that would be all. Also never, never, never believe a RV salesman when he/she says you can pull this with that! When looking for a RV look inside the cabinets for the GROSS weight of that unit and use that for your guide on what the unit weighs and NOT the ''dry weight'' listed for the RV. Nobody travels ''dry'' and nearly everybody comes much closer to the max weight over time. I'm sorry to be the bearer of bad news but I strongly believe in knowing what my tow vehicle can safely handle, always know what my rig weighs, and never excede the max or gross for either. With 5vers the weight on the hitch, called pin weight, is much more than the comporable hitch weight of a bumper pull so much care should be made on how much pin weight will be on your rear axle which is rated on the driver's door jam of the Tundra. It's soooo easy to excede that weight. Hope that gets you started on your investigation of what you can pull safely, good luck Gerry
Forget the effectively part. This might be illegal and negligent if a problem occurs and you will be 100% liable, no question. I read a story that someone's own insurance didn't even cover the accident because they had an illegal condition. The person had to foot the whole thing. I don't know the outcome, but losing everything I had to something this bad is not an option for us.
Most 37 foot 5ers average 13,000 to 15,000 lbs towing weight. Depending on how your Toyota Tundra is equipped (available with the largest engine, highest differential rating, heaviest spring set, tow equipment, etc.) this trailer will still exceed the tow ratings even if you carried nothing in the truck and nothing in the trailer. But you'll probably have passengers, gear, the fifth wheel hitch hardware AND the pin weight of the trailer (15% to 25% of the GTW-gross trailer weight), plus all the gear in the trailer, too. Then you do want some margin because wind and road conditions can cause that weight to be heavier as you roll down the road.
I have a 37+ foot 5er. I towed it with a 3/4 ton Ford with a big engine and matching transmission. The weight on the rear axle exceeded the Rear Axle Weight Rating AND the Gross Vehicle Weight Rating. I added air bags but found out they DO NOT improve the weight rating. Fortunately my truck could only be improved by adding the F-350 leaf spring pack and larger tires and wheels to support the new weight ratings and I was able to solve my problem. I was very lucky. Most times it requires a new tow vehicle.
I would NOT tow that trailer with a Tundra or any other 1/2 ton like a Titan, F-150, Dodge, Chevy or GMC 1500. Even smaller fifth wheels might require a 3/4 ton. You might find a small enough 5th wheel for a 1/2 ton but you also wanted effective and I would not call a truck at its max weight rating effective. If this were true I still be towing my old 27' travel trailer with my big Ford Expedition. That was a terrible tow, easily within limits even with filled with gear and passengers, but that gas engine was screaming and struggling on any hill.
Toyota Tundra Truck - 2011 Performance and Specifications This is Toyota's website spec's on a 2011 Tundra. Basically, as the others say, no way. It will Tow up to 8,100 LBS, your over. 1,500 LB payload, how much you can put into it, your over. The pin weight is more than that, then the hitch, wife, kids, gear and yourself. Total weight, with everything in the truck, can't be over 6,800 lbs. This is a crew cab, a regular cab will be a bit more. Still not enough.