Fla. Stat. § 155.06
Should a majority of all votes cast upon the question be in favor of establishing such county public hospital, or should the board of county commissioners of any county establish a county public hospital as provided in s. 155.05, the Governor of the state shall immediately proceed to appoint five trustees chosen from the citizens at large from such county, with reference to their fitness for such office, who shall constitute a board of trustees for said public hospital. On the original appointment of said trustees, two of said trustees shall be appointed for a term of 1 year, one for a term of 2 years, one for a term of 3 years, and one for a term of 4 years; and thereafter upon the expiration of said original appointments, their successors shall be appointed by the Governor of the state for terms of 4 years.
Fla. Stat. § 155.06