1
                                                                       Exhibit 5

                          DOMINICK'S SUPERMARKETS, INC.

               AMENDMENT TO CLASS A COMMON STOCK PURCHASE WARRANT


               This AMENDMENT TO CLASS A COMMON STOCK PURCHASE WARRANT, dated as
of October 13, 1998, between Dominick's Supermarkets, Inc., a Delaware
corporation (the "Company"), and The Yucaipa Companies, a California general
partnership ("Yucaipa"), amends that certain Class A Common Stock Purchase
Warrant No. W-1 dated as of March 22, 1995 of the Company, as amended, entitling
Yucaipa to purchase 3,874,491 shares (subject to adjustment) of common stock,
par value $.01 per share, of the Company (the "Warrant"). Capitalized terms used
herein without definition shall have the meanings assigned to them in the
Warrant.

               WHEREAS, the parties hereto have entered into the Warrant and
desire to amend certain provisions thereof, as more fully described herein;

               NOW, THEREFORE, in consideration of the premises, the parties
hereto hereby agree as follows:

               1. Restrictions on Transfer. Section 7(b) of the Warrant shall be
amended to read in its entirety as follows:

                      Transfer Restrictions. Neither this Warrant nor any
        interest herein may be directly or indirectly transferred or assigned by
        the Holder other than (i) to Ronald W. Burkle or a Controlling
        Stockholder controlled by Ronald W. Burkle and the equity holders of
        which consist solely of Ronald W. Burkle and Yucaipa Individuals or (ii)
        to Safeway Inc. or any of its wholly-owned subsidiaries, in connection
        with the transactions contemplated by that certain Agreement and Plan of
        Merger, dated as of October 13, 1998 (the "Merger Agreement"), among the
        Company, Safeway Inc. and Windy City Acquisition Corp. and that certain
        Stockholders Agreement, dated as of October 13, 1998, among Safeway
        Inc., Windy City Acquisition Corp. and the other parties listed on the
        signature pages thereto, upon the first to occur of (x) the Offer
        Consummation Date (as defined in the Merger Agreement) or (y) the
        effective time of the Merger (as defined in the Merger Agreement).




   2

               IN WITNESS WHEREOF, the parties hereto have caused this Amendment
to Class A Common Stock Purchase Agreement to be duly executed and delivered as
of the day and year first above written.

                                       DOMINICK'S SUPERMARKETS, INC.


                                       By: /s/ Robert A. Mariano
                                          --------------------------------------
                                       Name:  Robert A. Mariano
                                       Title: President and Chief Executive 
                                              Officer




                                       THE YUCAIPA COMPANIES


                                       By: /s/ Ronald W. Burkle
                                          --------------------------------------
                                       Name:  Ronald W. Burkle
                                       Title: Managing General Partner