The positions of Chief of Police Division and Chief of Fire Division shall be filled by competitive examination among qualified members of the respective divisions, and those other persons eligible to take the examination as provided in this section. The eligibility of members of each Division who can take the examination shall be determined by the Municipal Civil Service Commission. In addition the Mayor may nominate 2 additional qualified candidates from outside the Divisions to take the examination. The testing and appointment shall be made in accordance with Section 5.04 of this Charter.