Owners and operators of permanent amusement parks which shall be open for the public for not more than five months of each year may be exempted from payment of the license or privilege taxes on amusements or entertainments licensed by this title; provided, that they take out and pay for a license to operate a permanent amusement park at the following rates: In cities or towns of less than 5,000 inhabitants, or within five miles thereof, $25; in cities or towns of 5,000 inhabitants and less than 15,000 inhabitants, or within five miles thereof, $50; in cities of 15,000 and less than 25,000 inhabitants, or within five miles thereof, $100; in cities of 25,000 or more inhabitants, or within five miles thereof, $200. The provision of this title permitting the payment of a half-year license after April 1 shall not apply to this section. No license shall be paid under this section by any town or city which itself owns and operates an amusement park.