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


                                FORM 10-QSB


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

             For the quarterly period ended September 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
--------------------------------------------------------------------------------

                                                              September 30,
ASSETS                                                             1996
                                                            --------------------
CURRENT ASSETS                                                 (Unaudited)
<S>                                                                      <C>      
  Accounts receivable - oil & gas sales                       $          42,419   
  Other current assets                                                    3,656
                                                            --------------------

Total current assets                                                     46,075
                                                            --------------------

OIL & GAS PROPERTIES
  (Successful efforts accounting method) - Proved
   mineral interests and related equipment & facilities               3,480,304
  Less  accumulated depreciation and depletion                        3,284,074
                                                            --------------------

Property, net                                                           196,230
                                                            --------------------


TOTAL                                                          $        242,305   
                                                            ====================

LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accounts payable                                             $        32,122   
   Payable to general partner                                            26,166
                                                            --------------------

Total current liabilities                                                58,288
                                                            --------------------

NONCURRENT PAYABLE TO GENERAL PARTNER                                    78,498
                                                            --------------------

PARTNERS' CAPITAL:
   Limited partners                                                      67,449
   General partner                                                       38,070
                                                            --------------------

Total partners' capital                                                 105,519
                                                            --------------------

TOTAL                                                          $        242,305   
                                                            ====================


Number of $500 Limited Partner units outstanding                         10,797
</TABLE>



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

                                      I -1
<PAGE>
<TABLE>
<CAPTION>
ENEX OIL & GAS INCOME PROGRAM III - SERIES 5, L.P.
STATEMENTS OF OPERATIONS
----------------------------------------------------------------------------


(UNAUDITED)                            QUARTER ENDED                         NINE MONTHS ENDED
                                 -------------------------------------    ----------------------------------------

                                  September 30,        September 30,        September 30,         September 30,
                                      1996                  1995                 1996                  1995
                                 ----------------    -----------------    -----------------    -------------------

REVENUES:
<S>                               <C>                <C>                  <C>                  <C>               
  Oil and gas sales               $       90,285     $         85,160     $        283,979     $          274,569
                                 ----------------    -----------------    -----------------    -------------------

EXPENSES:
  Depreciation and depletion              16,472               27,814               45,831                 80,627
  Impairment of property                       -                    -              147,948                      -
  Lease operating expenses                45,977               53,548              146,170                148,256
  Production taxes                         5,149                4,625               16,767                 15,227
  General and administrative               8,929               10,319               32,095                 34,866
                                 ----------------    -----------------    -----------------    -------------------

Total expenses                            76,527               96,306              388,811                278,976
                                 ----------------    -----------------    -----------------    -------------------

INCOME (LOSS) FROM OPERATIONS             13,758              (11,146)            (104,832)                (4,407)
                                 ----------------    -----------------    -----------------    -------------------

OTHER INCOME:
  Gain on sale of property                 1,606                    -               33,244                      -
                                 ----------------    -----------------    -----------------    -------------------

NET INCOME (LOSS)                 $       15,364     $        (11,146)    $        (71,588)    $           (4,407)
                                 ================    =================    =================    ===================
</TABLE>



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

                                       I-2

<PAGE>
<TABLE>
<CAPTION>
ENEX OIL AND GAS INCOME PROGRAM III - SERIES 5, L.P.
STATEMENTS OF CASH FLOWS
----------------------------------------------------------------------------------------------

(UNAUDITED)
                                                       NINE MONTHS ENDED
                                                  --------------------------------------------

                                                     September 30,            September 30,
                                                          1996                    1995
                                                  -------------------      -------------------
CASH FLOWS FROM OPERATING ACTIVITIES:
<S>                                               <C>                        <C>                
Net (loss)                                        $          (71,588)        $         (4,407)  
                                                  -------------------      -------------------

Adjustments to reconcile net (loss) to
  net cash provided by operating activities:
  Depreciation, depletion and amortization                    45,831                   80,627
  Impairment of property                                     147,948                        -
  Gain on sale of property                                   (33,244)                       -
(Increase) decrease in:
  Accounts receivable - oil & gas sales                      (15,787)                   2,246
  Other current assets                                          (241)                  (1,239)
(Decrease) in:
   Accounts payable                                           (1,022)                  (4,870)
   Payable to general partner                                (62,469)                 (12,973)
                                                  -------------------      -------------------

Total adjustments                                             81,016                   63,791
                                                  -------------------      -------------------

Net cash provided by operating activities                      9,428                   59,384
                                                  -------------------      -------------------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Proceeds from sale of property                            35,098                        -
    Property additions - development costs                   (41,541)                  (9,389)
                                                  -------------------      -------------------

Net cash (used) by investing activities                       (6,443)                  (9,389)
                                                  -------------------      -------------------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Cash distributions                                        (16,265)                 (45,509)
                                                  -------------------      -------------------

NET INCREASE (DECREASE)  IN CASH                             (13,280)                   4,486

CASH AT BEGINNING OF YEAR                                     13,280                   10,432
                                                  -------------------      -------------------

CASH AT END OF PERIOD                             $                0        $          14,918   
                                                  ===================      ===================
</TABLE>




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

                                      I -3

<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. Effective August 1,
         1996 the  Company  sold its  interest  in the Spider  Lake 3-2 well for
         $1,606. The Company recognized a gain of $1,606 from the sale.

3.       A cash  distribution was made to the limited partners of the Company in
         the amount of $11,892,  representing  net revenues from the sale of oil
         and  gas  produced  from   properties   owned  by  the  company.   This
         distribution was made on July 31, 1996.

4.   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.   On  November  13,  1996,  the  Company  submitted   amended
     preliminary  proxy  material to the SEC with respect to this  consolidation
     The terms and  conditions  of the proposed  consolidation  are set forth in
     such preliminary proxy material.

5.   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>



Item 2.  Management's Discussion and Analysis or Plan of Operation.


Third Quarter 1995 Compared to Third Quarter 1996

Oil and gas  sales for the  third  quarter  increased  to  $90,285  in 1996 from
$85,160 in 1995. This represents an increase of $5,125 (6%). Oil sales decreased
by $488 (1%) A 28% decrease in oil  production  reduced  sales by $20,822.  This
decrease was partially  offset by a 38% increase in the average oil sales price.
Gas sales  increased  by $5,202  (50%).  A 55% increase in the average gas sales
price  increased  sales by $5,503.  This increase was  partially  offset by a 3%
decrease in gas production.  The changes in average sales prices correspond with
changes in the overall market for the sale of oil and gas. The lower oil and 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 decreased to $45,977 in 1996 from $53,548 in 1995. The
decrease of $7,571  (14%) is  primarily  due to workover  costs  incurred on the
Hightower and Corkscrew acquisitions in 1995.

Depreciation and depletion  expense decreased to $16,472 in the third quarter of
1996 from $27,814 in the third  quarter of 1995.  This  represents a decrease of
$11,342  (41%). A 22% decrease in the depletion  rate reduced  depreciation  and
depletion  expense by $4,679.  The changes in  production,  noted above  reduced
depreciation and depletion  expense by an additional  $6,663.  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.

Effective  August 1, 1996 the Company  sold its  interest in the Spider Lake 3-2
well for $1,606. The Company recognized a gain of $1,606 from the sale.

General and administrative  expenses decreased to $8,929 in the third quarter of
1996 from $10,319 in the third quarter of 1995. This decrease of $1,390 (13%) is
primarily  due to less  staff  time  being  required  to  manage  the  Company's
operations in 1996.

First Nine Months in 1995 Compared to First Nine Months in 1996

Oil and gas sales for the first nine months  increased  to $283,979 in 1996 from
$274,569  in 1995.  This  represents  an  increase  of  $9,410  (3%).  Oil sales
decreased by $620. A 14% decrease in oil  production  reduced  sales by $33,467.
This  decrease was  partially  offset by a 16% increase in the average oil sales
price.  Gas sales  increased by $9,619 (25%).  A 38% increase in the average gas
sales price increased sales by $13,451.  This increase was partially offset by a
10% decrease in gas production.  The changes in average sales prices  correspond
with  changes in the overall  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.

                                       I-5

<PAGE>


Lease operating  expenses decreased to $146,170 in the first nine months of 1996
from  $148,256 in the first nine months of 1995.  The decrease of $2,086 (1%) is
primarily due to the changes in production,  as noted above, partially offset by
road repair expenses incurred on the Corkscrew  acquisition in the first quarter
of 1996.

Depreciation and depletion expense decreased to $45,831 in the first nine months
of 1996  from  $80,627  in the first  nine  months of 1995.  This  represents  a
decrease of $34,796  (43%).  The changes in  production,  noted  above,  reduced
depreciation and depletion  expense by $10,795.  A 34% decrease in the depletion
rate reduced  depreciation and depletion expense by an additional  $24,001.  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.  Effective  August 1, 1996 the Company  sold its  interest in the
Spider Lake 3-2 well for $1,606.  The Company  recognized  a gain of $1,606 from
the sale.

General  and  administrative  expenses  decreased  to  $32,095 in the first nine
months  1996 from  $34,866 in the first nine  months of 1995.  This  decrease of
$2,771  (8%) is  primarily  due to less staff time being  required to manage the
Company's operations in 1996.


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.

                                       I-6

<PAGE>

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.  The Company did make  distributions  in the
amount of $11,892 on July 31, 1996. Future periodic  distributions will continue
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.  On
November 13, 1996, the Company submitted  amended  preliminary proxy material to
the SEC with  respect to this  consolidation.  The terms and  conditions  of the
proposed consolidation are set forth in such preliminary proxy material.

As of September 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>



                           PART II. OTHER INFORMATION


         Item 1.   Legal Proceedings.

                   None

         Item 2.   Changes in Securities.

                   None

         Item 3.   Defaults Upon Senior Securities.

                   Not Applicable

         Item 4.   Submission of Matters to a Vote of Security Holders.

                   Not Applicable

         Item 5.   Other Information.

                   Not Applicable

         Item 6.   Exhibits and Reports on Form 8-K.

                   (a)  There are no exhibits to this report.

                   (b)   The  Company  filed no  reports  on Form 8-K during the
                         quarter ended September 30, 1996.


                                      II-1

<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 13, 1996                           By: /s/ James A. Klein
                                                     James A. Klein
                                                 Controller and Chief
                                                  Accounting Officer


<PAGE>