Whenever any city shall own, purchase or otherwise acquire any cemetery or cemetery grounds, the mayor, by and with the consent of the council, shall appoint 5 trustees who shall be freeholders and electors in the city, and who shall constitute a “board of cemetery trustees.” The 5 trustees so appointed shall hold their offices for the term of 5 years, except that at the first appointment 1 shall be appointed for 1 year, 1 for 2 years, 1 for the term of 3 years, 1 for the term of 4 years and 1 for the term of 5 years from the first Monday in May of the year when appointed, and annually thereafter 1 trustee shall be appointed. The council may remove any trustee so appointed, for inattention to his duties, want of proper judgment, skill, or taste for the proper discharge of the duties required of him, or other good cause. Said board shall serve without compensation.