When a local option election in accordance with the provisions of this article or the former provisions of this article shall have been held in a county, another such election shall not be held in said county for a period of five years, and within that time the Racing Commission shall not accept or act upon any application for any other construction permit within said county, except that if an election be held seeking the approval of a permit for the construction of a horse racetrack another election may be held within such five-year period seeking the approval of a permit for the construction of a dog racetrack, and the reverse shall also be true. In the event a horse or dog racetrack shall be constructed in a county pursuant to a construction permit issued by the Racing Commission in accordance with the provisions of this article, no local option election shall thereafter be held as to any horse or dog racetrack constructed and established pursuant to such construction permit: Provided, That a local option election has been held for the type of racing to be conducted.