Stop and relax. Tire inflation is not something that requires charts and figuring and so much gnashing of teeth and biting of nails as some on this site would have you believe by their answers.
Every site has their "Sheldon Coopers" and this site is way over the top with them.
Do what most here said...inflate your tires when COLD to the max inflation on the sidewall.
Anything less only results in a slightly better (read softer) ride for the trailer and possibly for your TV but it's negligible.
Everything made has safety margins especially when they are safety related such as tires. The manufacturers consider these margins to be trade secrets and their lawyers will never let them be published, for good reason. But you can count on it that if the sidewall says 65 psi and a speed rating of 65mph the tire has been repeatedely tested to higher speeds without failure. The BIG reason for tire failure is UNDERINFLATION not overinflation.
I think it's a good idea to check your tires with a gauge before leaving your campsite/house etc everytime. (This means once a day while traveling) it's the last thing I do before I get in the truck and go.
So go have fun and don't obsess over so much of this stuff. It's not rocket science it's supposed to be fun.