Uhura WAS fifth in command, at least before Chekov's promotion to Lt. Commander. It's painfully obvious that DeSalle was only commanding the bridge for the first and only time in CATSPAW as to prevent Uhura from having the seat, and preventing Dr. McCoy's ancestors from having an embolism while watching the TV.
I'm not so sure.
After Kirk, Spock, and Scotty, the subsequent order of command was never clear. We don't know if Sulu was senior to Uhura or vice versa.
And we don't know if either of them was really next in line anyway. In the briefing room scene of "The Enterprise Incident," there are two silent officers in the background: a commander and a lieutenent commander. Maybe they were military intelligence aboard to track Kirk's mission, but maybe they were crew.
And there was Commander Giotto in "The Devil in the Dark." But maybe he was analogous to an officer of Marines aboard a Navy ship.
Still, it could be that Sulu and Uhura were not that senior, but just frequently seen on camera. The show always held about 400 unseen crew members in reserve for whatever type of personnel might be needed in a given story.