If pursuant to Section 5327 a district election is not held, the board of supervisors of the county in which the district, or the largest part thereof in area, is situated shall at its next regular meeting appoint to the positions of trustee those persons nominated, and such persons shall qualify, take office, and serve exactly as if elected at a general district election. If no person has been nominated, the board of supervisors shall appoint any qualified voter of the district to the position.