If, upon the hearing provided for in § 14-120-604, a petition is presented to the court signed by landowners against whose lands more than fifty percent (50%) in value of the assessment of benefits in a district is levied, or if the petition is presented to the court by the existing commissioners of the district, the court shall forthwith issue an order that the board of commissioners of the district shall thereafter consist of five (5) members, selected as hereinafter provided.