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                     U.S. SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

   
                                  FORM 10-KSB/A
                                  AMENDMENT II
    

                                   (Mark One)
               [X] ANNUAL REPORT UNDER SECTION 13 OR 15(d) OF THE
                 SECURITIES EXCHANGE ACT OF 1934 [FEE REQUIRED]

                   For the fiscal year ended December 31, 1995

             [ ] TRANSITION REPORT UNDER SECTION 13 OR 15(d) OF THE
                SECURITIES EXCHANGE ACT OF 1934 [NO FEE REQUIRED]

         For the transition period from...............to...............

                         Commission file number 33-34348-05

                              ENEX OIL & GAS INCOME
                           PROGRAM V - Series 5, L.P.
                 (Name of small business issuer in its charter)

           New Jersey                                        76-0303887
       (State or other jurisdiction of                      (I.R.S. Employer
       incorporation or organization)                      Identification No.)

             800 Rockmead Drive
            Three Kingwood Place
               Kingwood, Texas                                    77339
  (Address of principal executive offices)                     (Zip Code)

         Issuer's telephone number, including area code: (713) 358-8401

       Securities registered under Section 12(b) of the Exchange Act: None

         Securities registered under Section 12(g) of the Exchange Act:


                          Limited Partnership Interest

            Check whether the issuer (1) filed all reports  required to be filed
by  Section  13 or 15(d) of the  Exchange  Act during the past 12 months (or for
such shorter period that the registrant was required to file such reports),  and
(2) has been subject to such filing requirements for the past 90 days.

                                    Yes x No

            Check if there is no disclosure of delinquent  filers in response to
Item 405 of Regulation S-B is not contained in this form, and no disclosure will
be contained,  to the best of the registrant's knowledge, in definitive proxy or
information statements incorporated by reference in Part III of this Form 10-KSB
or any amendment to this Form 10-KSB.[x]

        State issuer's revenues for its most recent fiscal year. $470,696

            State  the  aggregate  market  value  of the  voting  stock  held by
non-affiliates  computed by  reference to the price at which the stock was sold,
or the average bid and asked prices of such stock as of a specified  date within
the past 60 days (See  definition  of  affiliate  in Rule 12b-2 of the  Exchange
Act):

                                 Not Applicable

                      Documents Incorporated By Reference:

                                      None

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     Conoco, Inc. accounted for 100% and 94% of the Company's total oil sales in
1995 and 1994, respectively. Although the Company marketed a significant portion
of its sales to the above noted company,  such a  concentration  does not pose a
significant risk due to the commodity nature of the Company's products.

   
     The  operators  of the  Company's  properties  are  noted  in Item 2 below.
Although a significant  portion of the Company's  properties  were operated by a
limited number of operators, this concentration does not pose a significant risk
since  the  Company's  rights  are  secured  by  joint  operating  agreements  .
Environmental and Conservation Regulation
    

     State  regulatory  authorities  in the  states  in which the  Company  owns
producing  properties  are empowered to make and enforce  regulations to prevent
waste of oil and to protect  correlative rights and opportunities to produce oil
for  owners of a common  reservoir.  Each of such  regulatory  authorities  also
regulates the amount of oil produced by assigning allowable rates of production,
which may be  increased  or  decreased  in  accordance  with  supply and demand.
Requirements  regarding  the  prevention  and clean- up of pollution and similar
environmental  matters are also  generally  applicable.  The costs,  if any, the
Company may incur in this regard cannot be predicted.

     The existence of such  regulations  has had no material  adverse effects on
the Company's  operations to date,  and the cost of compliance  has not yet been
material.  There are no material  administrative or judicial proceedings arising
under such laws or  regulations  pending  against  the  Company.  The Company is
unable to assess or predict the impact that  compliance with  environmental  and
pollution  control  laws  and  regulations  may have on its  future  operations,
capital expenditures, earnings or competitive position.

Tax Laws

     The  operations of the Company are affected by the federal  income tax laws
contained in the Internal  Revenue Code of 1986, as amended (the "Code").  Under
the Code,  generally,  the  Company  will  report  income  from the sale of oil,
against  which  it  may  deduct  its  ordinary  business  expenses,   depletion,
depreciation and intangible drilling and development costs.

     It is anticipated that most of the Company's income, if any, will be from a
"passive  activity"  for  purposes of the Code. A passive  activity  includes an
activity in which the taxpayer does not  materially  participate,  including the
ownership of a limited partnership interest, such as an interest in the Company.
"Passive  income," however,  does not include portfolio income (i.e.  dividends,
interest,  royalties,  etc.). Although taxpayers generally may not deduct losses
or use tax credits  derived from passive  activities  in an amount  greater than
their income derived from such activities, if and to the extent that the Company
generates  passive income,  it will be available to offset the limited partners'
passive losses from other sources.

   
     Partnerships  with  interests  that  are  "publicly  traded"  are  taxed as
corporations unless at least 90% of their income is "qualifying income." Passive
income  or  loss  from  Publicly  traded  partnerships  that  are not  taxed  as
corporations  generally  cannot be applied  against  passive income or less from
other  sources.  As  stated  in  Item  5 of  this  Annual  Report,  there  is no
established  public  trading  market  for  the  Company's  limited   partnership
interests. In addition, the Company derives more than 90% of its income from oil
and gas activities,  which  constitutes  qualifying income within the meaning of
section  7704(d) of the Code.  Therefore,  the Company should not be affected by
the publicly traded partnership rules.
    

                                      I-2
<PAGE>

                                   SIGNATURES


                  In  accordance  with Section 13 or 15 (d) of the Exchange Act,
the registrant caused this report to be signed on its behalf by the undersigned,
thereunto duly authorized.

                                      ENEX OIL AND GAS INCOME PROGRAM V -
                                             SERIES 5, L.P.

                                      By:    ENEX RESOURCES CORPORATION
                                              the General Partner



   
November 7, 1996                       By:     /s/   G. B. Eckley
                                              -------------------
                                                    G. B. Eckley, President


                  In  accordance  with the  Exchange  Act,  this report has been
signed  below on November 7, 1996,  by the following  persons in the capacities
indicated.
    


ENEX RESOURCES CORPORATION             General Partner


By:  /s/      G. B. Eckley

             ------------------------
              G. B. Eckley, President


     /s/      G. B. Eckley
                                        President, Chief Executive
              ------------------        Officer and Director


              G. B. Eckley


     /s/      R. E. Densford            Vice President, Secretary, Treasurer,
                                        Chief Financial Officer and Director
             -------------------


              R. E. Densford


     /s/      James A. Klein            Controller and Chief Accounting Officer

             -----------------

              James A. Klein



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