No vacation of a public street, public right-of-way or any part thereof having been duly accepted and recorded as part of a plat or subdivided tract shall take place unless the consent of the adjoining owners be obtained in writing and delivered to the public highway agency having jurisdiction over said public street or public right-of-way. Such public street or public right-of-way may, nevertheless, be vacated without such consent of the owners of the property abutting upon such public street or public right of way when such public street or public right-of-way has not been opened or used by the public for a period of five (5) years and when such nonconsenting owner or owners have access to the property from some other public street, public right-of-way or private road. However, before such order of vacation can be entered, it must appear to the satisfaction of the public highway agency that the owner or owners of the property abutting said public street or public right-of-way have been served with notice of the proposed abandonment in the same manner and for the same time as is now or may hereafter be provided for the service of the summons in an action at law. Any vacation of lands within one (1) mile of a city shall require written notification to the city by regular mail at least thirty (30) days prior to the vacation.