The "common wisdom" is not to run trailer tires more than 5 years old, no matter how good the tread and sidewalls look. The logic is that the tires dry out and become brittle with lack of use.
(Using tubes with tubeless tires is generally a bad idea. Increased heat and friction, etc.)
All that being said, I know several guys who are running "ancient" tires on their trailers who have had no problems. However, I also know several guys who have run tires 6-7 years old on car haulers and offroad trailers who have had blowouts at the worst possible time.
My personal opinion is that new trailer tires are cheap compared to the potential cost of repairing vehicle/trailer damage in the event an old tire suffers a catastrophic failure. Even if a blowout doesn't cause any vehicle/trailer damage, they always seem to happen in the middle of the night, in heavy traffic or on a twisty mountain road with no turnouts. Better to have new tires and some peace of mind.
My two cents.