The owners, agents or occupants of all lots and parcels of ground within the City limits shall cut or cause to be cut all offensive vegetation on their respective lots or parcels of ground not later than May 15, July 1 and August 15 of each year. In any case where the offensive vegetation is not cut within five (5) days after any date fixed above, it shall be the duty of the Zoning Enforcing Officer to enforce the provisions of this chapter. The provisions of this section also apply to all lands and lots abutting on any street or public way, to that portion of the property that lies between the property line of the property and the curb line, but only where curb and gutter have been installed.