Toyota Tundra - TT ?

6000 is on the yellow sticker on the actual trailer. Equalizer Hitch 10k would be used.

I think you'll be fine as well. Loaded up I would bet your tongue weight would be 1k or under. That leaves 500lbs for passengers, so unless they are really heavy you'll be fine. Pack everything in the TT and leave the truck bed empty if needed.

I suspect you'll be a little surprised at the ACTUAL weight of the trailer. If the brochure says 7000 lb. it'll likely be closer to 7500 before you begin loading anything in it. USUALLY any optional items are not included i the dry weight or UVW of the trailer which is used in the brochures. This often includes even "forced options" such as stab jacks, batteries, TV antennae, patio awning and many other common things. It is ALWAYS much better to consider the GVWR of any trailer you plan on towing and use 15% of that weight as the fully loaded tongue weight. You have a VERY capable truck but some models tend to be very light in the payload department so those are the numbers you need to check carefully. If the math works out then you're good to go.
Good luck / Skip

I have the 2013 Tundra and tow a Airstream with 700 lbs TW. He should use a weight distr. hitch.

The Tundra is a great truck, when used within its specs. Know your true tongue weight and make sure you have enough payload. If you have enough payload for your tongue weight, passengers and gear, the Tundra is a great choice. The 5.7 is a BEAST of an engine. Gas mileage will be about 9-11 mpg depending on terrain and speed. 26 gallon tank will have you stopping about every 240 miles or so. Its perfect for me, cause our 17 month old daughter usually needs a diaper or food every 3.5 hours or so.

only way to be sure is to weigh the tongue of the trailer, many times you can be surprised at a trailers weigh when fully loaded and ready to roll. also how you load the trailer, heavy front, heavy rear or balanced
trailer should have more weight to the front so truck does not bounce.

Toyota Tundra should be a fine Tow Vehicle

the tow vehicle rule:
tow no more than 80% of the maximum tow weight of the vehicle, remember pulling the load is not the major issue, its stopping the load when some fool pulls out in front of you, that is what stresses the truck and trailer.

good luck and stay safe.

Tundra owner here; He'll be good to go IMO. I'm pulling about 1,000 lbs heavier than that with my 2007.