Any applicant for a license or any licensee shall have the right to appeal within five days, to a Board of Appeals, from the refusal of the Mayor to grant an application for a license or the revocation by the Mayor of the license. The Board of Appeals shall consist of the President of Council, the Fiscal Officer and the Chief of Police. Notice of the appeal shall be filed in writing within the time hereinabove specified with the Fiscal Officer who shall act as the Secretary of the Board of Appeals.