N.M. Stat. § 19-10-12
The legal owners of all leases issued by the commissioner of public lands prior to the effective date of this amendment, containing provision, or provisions, for preference right to a new lease, or extension of the term thereof upon the expiration of the initial five-year term, and where valuable discoveries of the oil and gas have not been made, shall have an absolute preference right to such new lease or extension, upon the terms and conditions provided in such leases without paying a bonus therefor, and in the exercise of such preference right the provisions of Chapter 125 of the 1929 Session Laws [19-10-1, 19-10-12 to 19-10-25 NMSA 1978], and of this act [19-10-1, 19-10-12, 19-10-15 to 19-10-18, 19-10-22 NMSA 1978] relating to sales made upon competitive bidding by sealed bids, or at public auction, shall not apply in any case, but all such renewals, extensions or new leases made pursuant to such preference rights shall be only for a term of five years and as long thereafter as oil and gas in paying quantities, or either of them, is produced from the leased premises, and without further preference right to renewal or extension for successive terms.
NMS § 19-10-12