If a member or members of the Council, or any of them, designate in the petition, file with the Clerk of the Council within five days after said notice from the Clerk of the Council, his or their written resignation, the same shall be irrevocable and the Clerk of the Council shall at once notify the election authorities of the fact and the election authorities shall forthwith order and fix a day for holding a recall election for the removal of those not resigning. Such election shall be held not less than sixty nor more than ninety days after the expiration of the period of five days last mentioned, at the same time as any other general or special election held within such period; but if no general or special election be held within such period, the election authorities shall call a special recall election.