Would you trust 13 year old tires?

Nope, not me, not worth it. Manufacturer recommendations range from 5 to 10 years depending on the manufacturer. Over 10 years and they're junk, "roller" use only for me, good for rolling in-progress cars around my shop and property but no street use.

I've got a handful of leftover rims with roller tires on them, and I've literally seen a few of them explode in my yard, just sitting there. Off the car, no loads, just blow a belt right out of the tire with a loud bang.

Anything over 10 years old for a tire and you're just rolling the dice. Rubber oxidizes and ages even if it's not being used. It's just not worth it.