It's not a 5% chance. It's 5% that the event will happen, then the game chooses 10 tiles, so it's less than a 5% chance. Could be that IF the event is triggering (it could not be triggering at all), that your random tiles just don't have trees on them.
If you're that desperate I believe the new shop on Ginger Island sells mushroom tree seeds, just beware of the parrots.