Section 26. There shall be a board of registration in veterinary medicine, in sections twenty-seven and twenty-eight called the board, consisting of four veterinarians, and one representative of the public, subject to the provisions of section nine B. Each member of said board shall be a legal resident of the commonwealth. Each veterinarian member of said board shall be licensed to practice veterinary medicine in the commonwealth, a graduate of a school or college teaching veterinary medicine and approved by the approving authority, and shall have had at least five years’ experience in the active practice of veterinary medicine, surgery and dentistry prior to his appointment. No member shall be a member of any faculty in any institution having the power to confer degrees in veterinary medicine. One member thereof shall annually before December first be appointed by the governor, for five years from January first following. No veterinarian member appointed to a full five year term under this section shall be reappointed to succeed himself.