Section 5. The office of the chief justice of a department of the trial court, as provided in section one, shall not be deemed a judicial office as comprehended under the provisions of Article I of Chapter III of Part the Second of the Constitution. Said office of chief justice shall be filled by appointment, from among the justices appointed to the particular department, by the chief justice for administration and management. A chief justice shall hold said office for a term of five years, and shall be eligible to be reappointed for additional five-year terms. A chief justice, so appointed, may be removed from that office prior to the expiration of his term upon a determination by the chief justice for administration and management that such removal is in the best interests of the administration of justice.