Upon the filing of said petition mentioned in the preceding section, the court in its discretion and upon showing of benefit to the estate of said decedent or ward, shall make an order authorizing and directing said administrator, executor or guardian to sell a lease upon the lands therein described for oil and gas or other mining purposes, said sale to be at public auction to the highest bidder for cash and to be held in the courtroom of said court not less than five (5) days from the making of said order. Notice of such sale shall be given at least five (5) days before said sale by publication one time in a newspaper in said county, and where the lands involved belong to the estate of a deceased person, by mailing to the heirs of such deceased person, if their post office addresses be known. And if the lands to be leased are situated in any other county than that in which the probate proceeding is pending, then such notices as provided above for such period of time and place shall be published also in the county of the location of the lands.