After the election herein provided, boards of directors of such districts shall consist of five directors, one representing each election precinct of such district, and one director-at-large. All of such directors shall have equal powers and responsibilities. In case of vacancy through death, resignation, removal from the district or failure of any elected director to qualify, the remaining members of the board shall, by majority vote, fill such vacancy. The person selected to fill such vacancy shall hold such position until the next election of directors in such district. At the next election of directors of such district, following a vacancy, a director shall be elected to fill such vacancy.