A Zoning Board of Appeals is hereby created. Said Board shall consist of five members appointed by the Town Board, which shall also designate a Chairman. No person who is a member of the Town Board shall be eligible for membership on such Zoning Board of Appeals. Of the members of the Board first appointed, one shall hold office for the term of one year, one for the term of two years, one for the term of three years, one for the term of four years, and one for the term of five years, from and after his/her appointment. Their successors shall be appointed for the term of five years from and after the expiration of the terms of their predecessors in office. If a vacancy shall occur otherwise than by the expiration of the term, it shall be filled by the Town Board by appointment for the unexpired term.