Where the board of directors is to be composed of 3 directors, one of the directors shall hold office for one year, another for 2 years and another for 3 years from the first day of July following their appointment, but each until his successor is appointed, and at their first regular meeting they shall cast lots for the respective terms. Where the board of directors is to be composed of 5 directors, one of the directors shall hold office for one year, 2 for 2 years, and 2 for 3 years, from the first day of July following their appointment, but each until his successor is appointed, and at their first regular meeting they shall cast lots for the respective terms. Whenever additional directors to existing boards are appointed under the provisions of Section 5-23007, one of the additional directors shall hold office for 2 years and the other for 3 years from the first day of July following his appointment, but each until his successor is appointed, and the additional directors shall draw lots for their respective terms. Annually thereafter the presiding officer of the county board, with the advice and consent of the county board, shall, before the first day of July of each year, appoint as before one director, to take the place of the retiring director, who shall hold office for 3 years and until his successor is appointed. The chairman or president, as the case may be, of the county board may, by and with the consent of the county board, remove any director for misconduct or neglect of duty.