The five gates of the Temple mount were: the two Chuldah gates on the south, used for entry and exit; Kiponos on the west, used for entry and exit; Tadi on the north, which wasn’t used; and the east gate, on which there was a depiction of Shushan, the capital of the Persian empire. [This was in the second Temple, whose construction had been permitted by the Persian king Cyrus.] It was through this gate that the Kohein Gadol would burn the para adumah (red heifer), and through which the cow and those involved in the process would depart for the Mount of Olives.
There were seven gates in the courtyard:* three in the north, three in the south and one in the east. In the north: the fuel gate, the firstborn (animal) gate and the water gate. In the east was the Nikanor gate, which had two chambers, one on either side – the chamber of Pinchas the dresser (who was responsible for the uniforms of the kohanim) and the chamber of those who made the pan flour offerings. (The gates in the north are the subject of the next mishna.)
*Mishna 1:1 says guards were placed at the five gates of the courtyard. Either there is a difference of opinion as to the number of gates or two of them did not require guards posted. See Tamid 27a for full details.