The judgment for unpaid court costs in any court of this state shall cease to be a lien on real estate unless action has been brought thereon within (1) five years after the latest partial payment has been made thereon, or (2) five years after such case becomes inactive or is closed by final judgment. The lien of any unpaid costs as of February 20, 1974, which would otherwise be terminated by this section shall continue for one year from such date at which time it shall terminate unless an action has been brought thereon within such year.