(a) Cities of the first and second class and incorporated towns are given power and authority to vacate public streets and alleys within the cities and towns under the conditions and in the manner herein provided.
(b) In all cases where the owner of property within a city or town shall have dedicated, or may hereafter dedicate, a portion of the property to the public use as streets or alleys by platting the property and causing the plat to be filed for record, as provided by law, and any street or alley, or section thereof, shown on the plat so filed shall not have been actually used by the public as a street or alley for a period of five (5) years and in all cases where all property abutting any street or alley, or section thereof, is owned by any educational institution or college, whether the property shall have been actually used by the public as a street or alley for a period of five (5) years or not, the city or town council shall have power to vacate and abandon the street or alley, or any portion thereof, by proceeding in the manner set forth in this subchapter.