When the petition shall be found by the clerk to be sufficient, he shall submit the same, with his certificate, to the mayor and council without delay, and the mayor and council shall immediately notify the officer sought to be removed, and if the said officer does not resign within five (5) days after said notification, the mayor and council shall forthwith, after said five-day period, order and fix a date for holding the said election, not less than twenty (20) days nor more than thirty (30) days from the date of the clerk's certificate that a sufficient petition is filed.