Any private postsecondary career school offering instruction in the State of Nebraska shall, within five years of its initial authorization to operate, apply to the department for the accreditation of such school. No private postsecondary career school shall be accredited unless it submits to the department a written application for accreditation in accordance with the rules and regulations adopted and promulgated by the department pursuant to the Private Postsecondary Career School Act. Such application shall be accompanied by the fee provided in section 85-1643.