In all cases where the owner of lands situated in a county and outside of a city of the first or second class or incorporated town has dedicated a portion of the lands as streets, alleys, or roadways by platting the lands into additions or subdivisions and causing the plat to be filed for record in the county and any street, alley, or roadway, or portion thereof shown on the plat so filed shall not have been opened or actually used as a street, alley, or roadway for a period of five (5) years, or where any strip over the platted lands, although not dedicated as a street, has been used as a roadway, the county court shall have power and authority to vacate and abandon the street, alley, or roadway, or a portion thereof, by proceeding under the conditions and the manner provided in this chapter.