Though no action or suit is brought or pending, as provided in § 9-15-1, the district court may permit any persons or corporations who have any cause or causes of action not following the course of equity and the superior court may permit any persons or corporations who have any cause or causes of action, existing between them, to enter into a rule of court to refer the cause or causes of action to the decision of one or more referees, as provided in § 9-15-1, either jointly or severally, generally or specially; provided, that no rule entered into in the district court under the provisions of this chapter shall be made for any claim or claims which exceed in amount the sum of five thousand dollars ($5,000).