Your tires do not say "run at 80 psi." They likely say that 80 psi is the maximum cold tire pressure. You can run them at any pressure you like up to 80 but don't exceed 80 cold.
Your trailer manufacturer must have known the weight of the trailer and how much pressure the tires would need to support that weight and thus they have the 65 psi sticker.
To know anything for sure you would need to weigh the trailer, look up the tire inflation tables, and see how much inflation pressure is necessary for that weight. I suspect if you do that it will be around 65 psi, not 80 psi.
You can run 80 if you want but it will result in a harsher, more bouncy ride for the trailer.