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 March 31, 1997

                                       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

<PAGE>
                               PART I. FINANCIAL INFORMATION

Item 1. Financial Statements

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

                                                                  MARCH 31,
ASSETS                                                               1997
                                                          ------------------
                                                                (Unaudited)
CURRENT ASSETS:
<S>                                                          <C>             
  Cash                                                       $       17,668  
  Accounts receivable - oil & gas sales                              41,168
  Other current assets                                                2,731
                                                          ------------------

Total current assets                                                 61,567
                                                          ------------------

OIL & GAS PROPERTIES
  (Successful efforts accounting method) - Proved
   mineral interests and related equipment & facilities           3,494,967
  Less  accumulated depreciation and depletion                    3,288,049
                                                          ------------------

Property, net                                                       206,918
                                                          ------------------


TOTAL                                                        $      268,485  
                                                          ==================

LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accounts payable                                          $       29,271  
   Payable to general partner                                        89,622
                                                          ------------------

Total current liabilities                                           118,893
                                                          ------------------

PARTNERS' CAPITAL:
   Limited partners                                                 106,715
   General partner                                                   42,877
                                                          ------------------

Total partners' capital                                             149,592
                                                          ------------------

TOTAL                                                       $       268,485  
                                                          ==================


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.
STATEMENTS OF OPERATIONS
-----------------------------------------------------------------------------
<TABLE>
<CAPTION>

(UNAUDITED)                                THREE MONTHS ENDED
                                     ----------------------------------------
                                        MARCH 31,              MARCH 31,
                                           1997                  1996
                                   -------------------    -------------------
REVENUES:
<S>                                <C>                        <C>             
  Oil and gas sales                $          102,695         $       92,521  
                                   -------------------    -------------------

EXPENSES:
  Depreciation and depletion                    9,858                 13,893
  Impairment of property                            -                147,948
  Lease operating expenses                     50,591                 53,454
  Production taxes                              6,204                  5,719
  General and administrative                    8,544                 12,443
                                   -------------------    -------------------

Total expenses                                 75,197                233,457
                                   -------------------    -------------------

NET INCOME (LOSS)                  $           27,498         $     (140,936) 
                                   ===================    ===================
</TABLE>



See accompanying notes to financial statements.
------------------------------------------------------------------------------
                                       I-2

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

STATEMENT OF CHANGES IN PARTNERS' CAPITAL
FOR THE YEAR ENDED DECEMBER 31, 1996 AND
FOR THE THREE MONTHS ENDED MARCH 31, 1997
----------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                                                PER $500
                                                                                                 LIMITED
                                                                                                 PARTNER
                                                       GENERAL              LIMITED             UNIT OUT-
                                  TOTAL                PARTNER             PARTNERS             STANDING
                            -----------------    ------------------   ------------------   ------------------

<S>              <C>        <C>                  <C>                  <C>                  <C>              
BALANCE, JANUARY 1, 1996    $        193,372     $          27,479    $         165,893    $              15

CASH DISTRIBUTIONS                   (16,264)               (1,626)             (14,638)                  (1)

NET INCOME (LOSS)                    (55,014)               13,288              (68,302)                  (6)
                            -----------------    ------------------   ------------------   ------------------

BALANCE, DECEMBER 31, 1996           122,094                39,141               82,953                    8

NET INCOME                            27,498                 3,736               23,762                    2
                            -----------------    ------------------   ------------------   ------------------

BALANCE, MARCH 31, 1997     $        149,592     $          42,877    $         106,715 (1)$              10
                            =================    ==================   ==================   ==================
</TABLE>


(1)  Includes 2,064 units purchased by the general partner as a limited partner.



See accompanying notes to financial statements.
-----------------------------------------------------------------------------
                                       I-3

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

(UNAUDITED)
                                                                   THREE MONTHS ENDED
                                                             ------------------------------------------

                                                                MARCH 31,                MARCH 31,
                                                                   1997                    1996
                                                           -------------------      -------------------
CASH FLOWS FROM OPERATING ACTIVITIES:
<S>                                                        <C>                         <C>               
Net income (loss)                                          $           27,498          $      (140,936)  
                                                           -------------------      -------------------

Adjustments to reconcile net income (loss) to net cash
   provided by operating activities:
  Depreciation and depletion                                            9,858                   13,893
  Impairment of property                                                    -                  147,948
(Increase) decrease in:
  Accounts receivable - oil & gas sales                                (2,040)                 (12,158)
  Other current assets                                                    707                      132
Increase (decrease) in:
   Accounts payable                                                    (2,269)                 (18,675)
   Payable to general partner                                         (19,363)                   6,310
                                                           -------------------      -------------------

Total adjustments                                                     (13,107)                 137,450
                                                           -------------------      -------------------

Net cash provided (used) by operating activities                       14,391                   (3,486)
                                                           -------------------      -------------------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Property credits - development costs                                1,141                      228
                                                           -------------------      -------------------

NET INCREASE (DECREASE) IN CASH                                        15,532                   (3,258)

CASH AT BEGINNING OF YEAR                                               2,136                   13,280
                                                           -------------------      -------------------

CASH AT END OF PERIOD                                      $           17,668           $       10,022   
                                                           ===================      ===================

</TABLE>


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

                                       I-4

<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.   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 changes in the overall market for the sale of
     oil and gas and  significant  decreases in the  projected  production  from
     certain of the Company's oil and gas properties.

3.       On April 7, 1997, the Company's  General  Partner mailed proxy material
         to the limited partners 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 proxy
         material.

                                       I-5

<PAGE>



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

First Quarter 1997 Compared to First Quarter 1996

Oil and gas  sales for the  first  quarter  increased  from  $92,521  in 1996 to
$102,695  in 1997.  This  represents  an increase  of $10,174  (11%).  Oil sales
increased  by $13,595 or 18%. A 40%  increase  in the  average  oil sales  price
increased sales by $25,218.  This increase was partially offset by a 16% decline
in oil  production.  Gas sales decreased by $3,421 or 19%. A 46% decrease in gas
production reduced sales by $8,491.  This decrease was partially offset by a 51%
increase in the average gas sales  price.  The  decrease in oil  production  was
primarily  a  result  of  natural  production  declines.  The  decrease  in  gas
production  was due to sale of the Kidd well on the Enexco  acquisition in April
1996,  the sale of the Harper well in the RIC  acquisition in June 1996, and the
sale of the  Spider  Lake  well in the  RIC  acquisition  in  August  1996.  The
increases  in the  average  oil and gas  prices  were due to  relatively  higher
production from properties with a higher average sales price coupled with higher
prices in the overall market for the sale of oil and gas.

Lease operating  expenses decreased from $53,454 in the first quarter of 1996 to
$50,591 in the first  quarter of 1997.  The decrease of $2,863 (5%) is primarily
due the changes in production, noted above.

Depreciation and depletion  expense  decreased from $13,893 in the first quarter
of 1996 to $9,858 in the first  quarter of 1997.  This  represents a decrease of
$4,035 (29%). The changes in production,  noted above,  reduced depreciation and
depletion  expense  by $3,012.  A 9%  decrease  in the  depletion  rate  reduced
depreciation and depletion  expense by an additional  $1,023.  The rate decrease
was  primarily  due to an upward  revision  of the oil and gas  reserves  during
December 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 changes in the overall market for the sale of oil
and gas and  significant  decreases in the projected  production from certain of
the Company's oil and gas properties.

General and administrative  expenses decreased from $12,443 in the first quarter
of 1996 to $8,544 in the first  quarter of 1997.  This decrease of $3,899 or 31%
was  primarily  due to less staff time being  required  to manage the  Company's
operations  in 1997,  coupled  with a $1,859  decrease  in the  amount of direct
expenses incurred by the Company.

                                       I-6

<PAGE>



CAPITAL RESOURCES AND LIQUIDITY

On April 7, 1997,  the Company's  General  Partner  mailed proxy material to the
limited partners 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 proxy material.

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 1996 to 1997 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,   financing  and  investing
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, 1996
reserve  report  prepared by Gruy,  there  appears to be  sufficient  future net
revenues to pay all  obligations  and  expenses.  The Company does not intend to
purchase additional properties or fund extensive development of existing oil and
gas properties,  and as such; has no long-term  liquidity  needs.  The Company's
projected cash flows from operations will provide  sufficient funding to pay its
operating expenses and debt obligations.  The general partner does not intend to
accelerate the repayment of the debt beyond the cash flow provided by operating,
financing and investing activities. Based upon current projected cash flows from
its property,  it does not appear that the Company will have  sufficient cash to
pay distributions and pay its operating expenses, and meet its debt obligations.
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.

As of March 31,  1997,  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 March 31, 1997.


                                      II-1

<PAGE>

                                  SIGNATURES


      Pursuant to the  requirements of the Securities  Exchange Act of 1934, the
Registrant  has duly  caused  this  Report  to be  signed  on its  behalf by the
undersigned hereunto duly authorized.


                                                     ENEX OIL & GAS INCOME
                                                     PROGRAM III - 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




May 11, 1997                                      By: /s/ James A. Klein
                                                     -------------------
                                                          James A. Klein
                                                       Controller and Chief
                                                        Accounting Officer