Section 54. There shall be a board of registration of real estate brokers and salesmen, in this section and in sections fifty-five to fifty-seven, inclusive, called the board, to be appointed by the governor, with the advice and consent of the council, consisting of five members, citizens of the commonwealth, three of whom shall have been actively engaged in the real estate business as a full-time occupation for at least seven years prior to their appointment and who shall be licensed real estate brokers, and two of whom shall be representatives of the public. The governor shall designate the chairman. As the term of office of a member of the board expires, his successor shall be appointed by the governor, with like advice and consent, to serve for five years. Each member shall be eligible for reappointment and shall serve until the qualification of his successor. The governor may also, with like advice and consent, fill any vacancy in the board for the unexpired portion of the term.