The City Officer may enter upon any private property and abate any nuisance found thereon, or in front thereof, more than seven (7) days after Notice to Abate such nuisance has been posted as required by this Chapter, if no person has filed a written statement of objections as herein provided within five (5) days thereafter. In the event objections have been duly filed, and overruled by the City Council, such officer may enter upon any private property and abate any nuisance found thereon, or in front thereof, in accordance with the order of the City.