Any tips for towing a car carrier?

It will be my first time towing with the Tundra! I have towed lightweight trailers with various cars, vans, and a wrangler 20+ years ago, but like the title says i'm looking for any tips or concerns i should be aware of while towing a 5,000 LB car on a car carrier 30 miles (not dolly, front and rear axles will be ON the trailer as it is AWD)...
Obvious stuff i'm considering / aware of:

• Drive defensively and keep a safe following distance (i'll be increasing following distance as the load / stopping distance will be increased)
• Use the tow/haul feature (since i usually do anyway)
• I'll air up my tires slightly to ensure they aren't overwhelmed (usually run mid 30's and would feel more comfortable with 38-42 for towing)
• it will be mostly flat land, but i've heard something about putting it in S4(?) though i'm not sure it will be necessary
• Not to age myself, but i've never backed up a trailer using a vehicle with a back up camera! lol, i will likely go old school and look through the back as i am hoping that backing up a trailer is still somewhere in my muscle memory!
• i have a 2018 CrewMax so i think i have the coveted transmission cooler, LOL!
• i'm considering putting my front anti-sway bar back on as i will be traveling about 30 miles with unknown traffic and road conditions (?) with the vehicle on board and returning with an empty trailer.

i'm more excited than concerned and i'm not trying to overthink it, but you guys have saved me (and plenty of others) in the past on other issues, so i thought i'd throw it out there (after searching and not seeing any obviously similar threads).

Anywho, thanks in advance and happy holidays!

 

You should not have any issues. Folks often use s4 or s5 to keep the trans from hunting gears- keeps it cooler and the convertor locked.
Id reinstall the sway bar
Look- don't rely on the rear camera only for reverse
Take your time, keep speeds around 65

This is a sticky and has some good info
https://www.tundras.com/threads/tow-ratings-guide-how-to-be-safe.39211/#post-2266953

 

What type of trailer brakes?

 

Just the emergency break away kind. So none for normal situations.


Trailer weighed in around 2,000 lbs allegedly
Cars curb weight is 3902

I did reinstall my front sway bar and bumped up tire pressure prior to towing.

Everything went great. Brakes actually felt good and strong though I never had to brake hard. Dd 10” exhaust sounded glorious. Truck was stable and pulled like a champ.