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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 0-16553

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

           New Jersey                                           76-0214445
 (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. $ 312,547

            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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     Sunniland Pipe Line Company and American  Exploration Company accounted for
25% and 23%,  respectively,  of the total  oil and gas sales in 1995.  Sunniland
Pipe Line Company and American  Exploration  Company  accounted for 26% and 22%,
respectively,  of the  total  oil and gas  sales  in 1994.  No  other  purchaser
individually  accounted  for more than 10% of such sales.  Although  the Company
marketed a significant portion of its sales to the above noted companies, 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 gas and to protect correlative rights and opportunities
to produce oil and gas for owners of a common reservoir. Each of such regulatory
authorities  also  regulates  the amount of oil and gas  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 and gas,  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.
    


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                                   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 III -
                                             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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