I chose to setup our PGA majors league by eliminating the worst score and only counting 5 players. Can you tell me if this is per round or per tournament?

The player whose score will be dropped will be the one that is doing the worst for the whole tournament.

It does not determine it by day, so the player (or players) being dropped can change throughout the tournament and the site removes the worst player in real time. However, it is only the player (or players) who ended up with the worst scores at the end of the tournament that will be dropped.