United States
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


   
                                   FORM 10-QSB/A
    


              [X] QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                  For the quarterly period ended June 30, 1996

                                       OR

             [ ] TRANSITION REPORT UNDER SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

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

                         Commission file number 0-16553

               ENEX OIL & GAS INCOME PROGRAM III - SERIES 5, L.P.
        (Exact name of small business issuer as specified in its charter)

                       New Jersey                           76-0214445
           (State or other jurisdiction of               (I.R.S. Employer
              incorporation or organization)            Identification No.)

                         Suite 200, Three Kingwood Place
                              Kingwood, Texas 77339
                    (Address of principal executive offices)


                           Issuer's telephone number:
                                 (713) 358-8401

     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

Transitional Small Business Disclosure Format (Check one):

                            Yes        No x


<PAGE>


                               PART I. FINANCIAL INFORMATION

Item 1. Financial Statements
<TABLE>
<CAPTION>

ENEX OIL & GAS INCOME PROGRAM III - SERIES 5, L.P.
BALANCE SHEET
------------------------------------------------------------------------------

                                                                JUNE 30,
ASSETS                                                            1996
                                                               ---------------
                                                               (Unaudited)
CURRENT ASSETS:
<S>                                                               <C>
  Cash                                                            $     4,515
  Accounts receivable - oil & gas sales                                42,662
  Other current assets                                                 36,833
                                                               ---------------

Total current assets                                                   84,010
                                                               ---------------

OIL & GAS PROPERTIES
  (Successful efforts accounting method) - Proved
   mineral interests and related equipment & facilities             3,505,157
  Less  accumulated depreciation and depletion                      3,311,932
                                                               ---------------

Property, net                                                         193,225
                                                               ---------------


TOTAL                                                             $   277,235
                                                               ===============

LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accounts payable                                               $    34,048
   Payable to general partner                                          27,353
                                                               ---------------

Total current liabilities                                              61,401
                                                               ---------------

NONCURRENT PAYABLE TO GENERAL PARTNER                                 109,414
                                                               ---------------

PARTNERS' CAPITAL:
   Limited partners                                                    69,907
   General partner                                                     36,513
                                                               ---------------

Total partners' capital                                               106,420
                                                               ---------------

TOTAL                                                            $    277,235
                                                               ===============


   
Number of $500 Limited Partner units outstanding                      10,797
    

</TABLE>





See accompanying notes to financial statements.
------------------------------------------------------------------------------

                                      I -1
<PAGE>

ENEX OIL & GAS INCOME PROGRAM III - SERIES 5, L.P.

NOTES TO UNAUDITED FINANCIAL STATEMENTS

1.       The  interim  financial   information  included  herein  is  unaudited;
         however,  such information reflects all adjustments  (consisting solely
         of  normal  recurring   adjustments)  which  are,  in  the  opinion  of
         management,  necessary  for a fair  presentation  of  results  for  the
         interim periods.

2.       Effective April 1, 1996, the Company sold its interest in the Kidd well
         in the Enexco acquisition for $17,920. The Company recognized a $17,920
         gain  from the sale.  Effective  June 1,  1996,  the  Company  sold its
         interest in the Harper well in the RIC  acquisition  for  $15,572.  The
         Company recognized a gain of $13,718 from the sale.

3.       On August 9, 1996, the Company's General Partner submitted  preliminary
         proxy material to the Securities  Exchange Commission with respect to a
         proposed  consolidation  of the Company with 33 other  managed  limited
         partnerships.  The terms and  conditions of the proposed  consolidation
         are set forth in such preliminary proxy material.

   
4.   The Financial  Accounting Standards Board has issued Statement of Financial
     Accounting  Standard  ("SFAS") No. 121,  "Accounting  for the Impairment of
     Long-Lived  Assets  and for  Long-Lived  Assets to be  Disposed  Of," which
     requires  certain assets to be reviewed for impairment  whenever  events or
     circumstances indicate the carrying amount may not be recoverable. Prior to
     this pronouncement,  the Company assessed properties on an aggregate basis.
     Upon  adoption of SFAS 121, the Company  began  assessing  properties on an
     individual  basis,  wherein  total  capitalized  costs may not  exceed  the
     property's  fair market  value.  The fair market value of each property was
     determined by H. J. Gruy and  Associates,  ("Gruy").  To determine the fair
     market value, Gruy estimated each property's oil and gas reserves,  applied
     certain  assumptions  regarding price and cost  escalations,  applied a 10%
     discount factor for time and certain discount  factors for risk,  location,
     type   of   ownership   interest,   category   of   reserves,   operational
     characteristics,  and other  factors.  In the first  quarter  of 1996,  the
     Company recognized a non-cash impairment  provision of $147,948 for certain
     oil and gas properties due to market  indications that the carrying amounts
     were not fully recoverable.
    


                                       I-4

<PAGE>

market for the sale of oil and gas. The lower oil  production  was primarily the
result of natural production  declines,  partially offset by production from the
Corkscrew  acquisition  which had been shut-in during the second quarter of 1995
for rod repairs.  The lower gas  production was primarily the result of the sale
of the Kidd well in the Enexco  acquisition,  effective  April 1, 1996,  coupled
with natural production declines.

Lease operating  expenses  increased to $100,193 in the first six months of 1996
from  $94,708 in the first six months of 1995.  The  increase  of $5,485 (6%) is
primarily due to road repair expenses  incurred on the Corkscrew  acquisition in
the first quarter of 1996.

Depreciation and depletion  expense decreased to $29,359 in the first six months
of 1994 to $52,813 in the first six months of 1995.  This  represents a decrease
of $23,454 (44%). The changes in production,  noted above,  reduced depreciation
and depletion  expense by $4,103.  A 40% decrease in the depletion  rate reduced
depreciation and depletion expense by an additional  $19,351.  The rate decrease
was primarily due to the lower property basis  resulting from the recognition of
an impairment of property for $147,948 in the first quarter of 1996.

   
The  Financial  Accounting  Standards  Board has issued  Statement  of Financial
Accounting  Standard  ("SFAS")  No.  121,  "Accounting  for  the  Impairment  of
Long-Lived  Assets and for Long- Lived Assets to be Disposed Of," which requires
certain assets to be reviewed for impairment  whenever  events or  circumstances
indicate  the   carrying   amount  may  not  be   recoverable.   Prior  to  this
pronouncement,  the Company  assessed  properties  on an aggregate  basis.  Upon
adoption of SFAS 121, the Company  began  assessing  properties on an individual
basis, wherein total capitalized costs may not exceed the property's fair market
value.  The fair market value of each property was  determined by H. J. Gruy and
Associates,  ("Gruy").  To determine the fair market value,  Gruy estimated each
property's oil and gas reserves, applied certain assumptions regarding price and
cost  escalations,  applied a 10% discount factor for time and certain  discount
factors for risk,  location,  type of ownership interest,  category of reserves,
operational  characteristics,  and other factors.  In the first quarter of 1996,
the Company recognized a non-cash  impairment  provision of $147,948 for certain
oil and gas properties due to market  indications that the carrying amounts were
not fully recoverable.
    


Effective  April 1, 1996,  the Company sold its interest in the Kidd well in the
Enexco  acquisition for $17,920.  The Company recognized a $17,920 gain from the
sale.  Effective  June 1, 1996, the Company sold its interest in the Harper well
in the RIC  acquisition  for $15,572.  The Company  recognized a gain of $13,718
from the sale.

General and administrative expenses decreased to $23,166 in the first six months
1996 from $24,547 in the first six months of 1995.  This decrease of $1,381 (6%)
is  primarily  due to less  staff time being  required  to manage the  Company's
operations in 1996.

                                      I-6

<PAGE>


CAPITAL RESOURCES AND LIQUIDITY

   
The Company's cash flow from  operations is a direct result of the amount of net
proceeds  realized  from the sale of oil and gas  production.  Accordingly,  the
changes in cash flow from 1995 to 1996 are  primarily  due to the changes in oil
and  gas  sales  described  above.  It is the  general  partner's  intention  to
distribute  substantially  all of  the  Company's  available  cash  flow  to the
Company's partners.  The Company's "available cash flow" is essentially equal to
the net amount of cash provided by operating activities.

The  Company  discontinued  the payment of  distributions  during  1995.  Future
distributions  are dependent  upon,  among other  things,  an increase in prices
received for oil and gas. The Company will  continue to recover its reserves and
distribute  to the limited  partners the net proceeds  realized form the sale of
oil and gas  production.  Distribution  amounts  are  subject  to  change if net
revenues  are  greater or less than  expected.  Based on the  December  31, 1995
reserve  report  prepared by Gruy,  there  appears to be  sufficient  future net
revenues to pay all  obligations  and  expenses.  The General  Partner  does not
intend to accelerate  the  repayment of the debt beyond the Company's  cash flow
provided by operating  activities.  Future periodic  distributions  will be made
once sufficient net revenues are  accumulated.  Company will continue to recover
its reserves and  distribute to the limited  partners the net proceeds  realized
form the sale of oil and gas  production.  Distribution  amounts  are subject to
change if net  revenues  are  greater  or less than  expected.  Future  periodic
distributions will be made once sufficient net revenues are accumulated.
    

On August 9, 1996, the Company's  General Partner  submitted  preliminary  proxy
material  to the  Securities  Exchange  Commission  with  respect  to a proposed
consolidation  of the Company with 33 other managed  limited  partnerships.  The
terms  and  conditions  of the  proposed  consolidation  are set  forth  in such
preliminary proxy material.

As of June 30,  1996,  the  Company  had no  material  commitments  for  capital
expenditures.  The  Company  does  not  intend  to  engage  in  any  significant
developmental drilling activity.

                                       I-7

<PAGE>



                                   SIGNATURES


         In accordance with the requirements of the Exchange Act, the registrant
caused this report to be signed on its behalf by the undersigned  thereunto duly
authorized.


                                                  ENEX OIL & GAS INCOME
                                             PROGRAM III - SERIES 5, L.P.
                                                      (Registrant)



                                              By:ENEX RESOURCES CORPORATION
                                                     General Partner



                                              By: /s/ R. E. Densford
                                                      R. E. Densford
                                                Vice President, Secretary
                                              Treasurer and Chief Financial
                                                         Officer




   
November 7, 1996                              By: /s/ James A. Klein
                                                 -------------------
                                                       James A. Klein
                                                   Controller and Chief
                                                    Accounting Officer