The Council may remove the Mayor for gross misconduct, malfeasance, misfeasance or nonfeasance in or disqualification for office, or for the conviction while in office of a crime involving moral turpitude, or if adjudicated legally incompetent, or for a violation of his or her oath of office, provided, however, that such removal shall not take place without the affirmative vote of five members of Council nor until the Mayor shall have been notified in writing of the charge against him or her at least ten days in advance of a public hearing upon such charge, and he or she or his or her counsel has been given an opportunity at such hearing to be heard, present evidence, and examine any witness appearing in support of the charge.