I read the rules and it said all use of emulators are banned because it gives an unfair advantage but later down in the rules it says that the dolphin emulator 5.0 is approved. I am confused as to whether or not I can use dolphin in the run and it still count if I submit it.

You may run the game on Dolphin 5.0 as that's the only approved emulator for this game at this moment in time. All emulators run differently than official hardware so by default they are hidden on most boards. While the run will be accepted should it be played on Dolphin (and you must show the entire window of Dolphin when recording), just know it will be inaccurate in comparison to a run on console.