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

   
                                  FORM 10-KSB/A
                                  AMENDMENT III
    

                                   (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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<PAGE>

                                     PART II


Item 5.      Market for Common Equity and Related Security Holder Matters

Market Information

             There is no  established  public  trading  market for the Company's
outstanding limited partnership interests.



Number of Equity Security Holders

                                               Number of Record Holders
               Title of Class                    (as of March 1, 1996)

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


          General Partner's Interests                      1

          Limited Partnership Interests                  1,771



Dividends

          The Company made cash  distributions to partners of $4 and $8 per $500
investment in 1995 and 1994 respectively.  The Company  discontinued the payment
of  distributions  in the  third  quarter  of  1995.  Future  distributions  are
dependent upon,  among other things,  an increase in the prices received for oil
and  gas.  The  Company  will  continue  to  recover  its  reserves  and  reduce
obligations in 1996. Based upon current  projected cash flows from its property,
it does not appear that the  Company  will have  sufficient  net cash flow after
debt service to pay distributions.

                                      II-1


<PAGE>




Item 6.     Management's Discussion and Analysis or Plan of Operation


Results of Operations

            This  discussion  should be read in  conjunction  with the financial
statements of the Company and the notes thereto included in this Form 10-KSB.

            Oil and gas sales in 1995 were $312,547 as compared with $374,421 in
1994.  This  represents  a decrease of $61,874 or 17%.  Oil sales  decreased  by
$43,088 or 14%. A 23%  decline in oil  production  caused  sales to  decrease by
$71,218. This decrease was partially offset by a 12% increase in the average oil
sales  price.  Gas sales  decreased  by $18,786 or 26%.  A 17%  decrease  in gas
production  reduced  sales by $11,976,  while a 12%  decrease in the average gas
sales price lowered sales by an additional  $6,810. The lower oil production was
primarily  the result of the shut-in of  production  in August,  1995,  from the
Corkscrew  acquisition in Florida due to hurricane  damage.  The decrease in gas
production  was  primarily a result of natural  production  declines  which were
especially pronounced on the RIC acquisition. The changes in average oil and gas
sales prices  correspond  with changes in the overall market for the sale of oil
and gas.

            Lease  operating  expenses  increased  to  $191,678  in  1995,  from
$187,056  in 1994.  The  increase  of  $4,622  or 2% was  primarily  a result of
workover  expenses  incurred on the Corkscrew  acquisition  to repair  hurricane
damage in 1995.

            Depreciation and depletion expense decreased to $87,220 in 1995 from
$109,477 in 1994.  This  represents a decrease of $22,257 or 20%. The changes in
production,  noted above,  caused depreciation and depletion expense to decrease
by $24,207. This decrease was partially offset by a 2% increase in the depletion
rate. The depletion rate increase was primarily due to downward revisions of the
oil  reserves  during  1995,  partially  offset by upward  revisions  of the gas
reserves during 1995.

   
            Effective October 1, 1995, the Company sold its interest in the Kidd
#1 well in the Enexco  acquisition to Humphrey Oil Co. for $54,600.  A gain from
the sale of $48,589 was  recognized  by the Company.  The impact of this sale on
current and future  revenues is not expected to be material,  as such  interests
represented approximately 2% of historical and future net revenues.
    

            General and  administrative  expenses  decreased  to $52,387 in 1995
from $60,664 in 1994.  The decrease of $8,277 or 14% was  primarily  due to less
staff time being required to manage the Company's operations.


Capital Resources and Liquidity

            The  Company's  cash flow from  operations is a direct result of the
amount of net proceeds from the sale of oil and gas production  after payment of
its debt  obligations.  Accordingly,  the changes in cash flow from 1994 to 1995
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 net cash flow to the Company's partners.

                                      II-2

<PAGE>



   
            The Company  discontinued  the payment of distributions in the third
quarter of 1995. Future  distributions are dependent upon among other things, an
increase in the prices  received for oil and gas.  The Company will  continue to
recover its reserves and reduce its  obligations  in 1996.  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. The Company plans to
repay the amount owed to the general partner over a five year period. 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 in the next twelve months.
    

            At December 31, 1995,  the Company had no material  commitments  for
capital  expenditures.  The Company does not intend to engage in any significant
developmental drilling activity.

                                      II-3

<PAGE>



Item 7.      Financial Statements and Supplementary Data



INDEPENDENT AUDITORS' REPORT


The Partners
Enex Oil & Gas Income
  Program III - Series 5, L.P.:


We have audited the accompanying  balance sheet of Enex Oil & Gas Income Program
III - Series 5, L.P. (a New Jersey limited  partnership) as of December 31, 1995
and the related statements of operations, changes in partners' capital, and cash
flows for each of the two years in the period ended  December  31,  1995.  These
financial statements are the responsibility of the general partner of Enex Oil &
Gas Income  Program  III - Series 5, L.P.  Our  responsibility  is to express an
opinion on the financial statements based on our audits.

We  conducted  our  audits  in  accordance  with  generally   accepted  auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement.  An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements.  An audit also includes
assessing the  accounting  principles  used and  significant  estimates  made by
management,  as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

In our  opinion,  such  financial  statements  present  fairly,  in all material
respects,  the financial  position of Enex Oil & Gas Income Program III - Series
5, L.P. at December  31,  1995 and the  results of its  operations  and its cash
flows  for each of the two  years  in the  period  ended  December  31,  1995 in
conformity with generally accepted accounting principles.


DELOITTE & TOUCHE  LLP




Houston, Texas
March 18, 1996

                                      II-4

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

BALANCE SHEET, DECEMBER 31, 1995
------------------------------------------------------------------------------

ASSETS
                                                                      1995
                                                                --------------
CURRENT ASSETS:
<S>                                                             <C>          
  Cash                                                          $      13,280
  Accounts receivable - oil & gas sales                                26,632
  Other current assets                                                  3,415
                                                                --------------

Total current assets                                                   43,327
                                                                --------------

OIL & GAS PROPERTIES
  (Successful efforts accounting method) - Proved
   mineral interests and related equipment & facilities             3,554,081
  Less  accumulated depreciation and depletion                      3 203,759
                                                                --------------

Property, net                                                         350,322
                                                                --------------

TOTAL                                                           $     393,649
                                                                ==============

LIABILITIES AND PARTNERS' CAPITAL (DEFICIT)

CURRENT LIABILITIES:
   Accounts payable                                             $      33,144
   Payable to general partner                                         167,133
                                                                --------------

Total current liabilities                                             200,277
                                                                --------------

PARTNERS' CAPITAL (DEFICIT):
   Limited partners                                                   165,893
   General partner                                                     27,479
                                                                --------------

Total partners' capital                                               193,372
                                                                --------------

TOTAL                                                           $     393,649
                                                                ==============


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



See accompanying notes to financial statements.
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                                      II-5
    

<PAGE>

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

NOTES TO FINANCIAL STATEMENTS
FOR THE TWO YEARS ENDED DECEMBER 31, 1995

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1.           PARTNERSHIP ORGANIZATION

             Enex Oil & Gas Income Program III - Series 5, L.P. (the "Company"),
             a New Jersey limited  partnership,  commenced  operations on August
             11,  1987  for  the  purpose  of  acquiring   proved  oil  and  gas
             properties. Total limited partner contributions were $5,398,602, of
             which  $53,986  was  contributed  by  Enex  Resources   Corporation
             ("Enex"), the general partner.

             In  accordance  with the  partnership  agreement,  the Company paid
             commissions  of  $517,721  for  solicited   subscriptions  to  Enex
             Securities  Corporation,  a subsidiary of Enex, and reimbursed Enex
             for organization expenses of approximately $162,000.

             Information  relating  to the  allocation  of  costs  and  revenues
             between Enex, as general  partner,  and the limited  partners is as
             follows:
                                                                     Limited
                                                            Enex     Partners

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


             Commissions and selling expenses                            100%
             Company reimbursement of organization
               expense                                                   100%
             Company property acquisition                                100%
             General and administrative costs                10%          90%
             Costs of drilling and completing
               development wells                             10%          90%
             Revenues from temporary investment of
               partnership capital                                       100%
             Revenues from producing properties              10%          90%
             Operating costs (including general and
               administrative costs associated with
               operating producing properties)               10%          90%

             At the point in time  when the cash  distributions  to the  limited
             partners  equal  their  subscriptions  ("payout"),   the  costs  of
             drilling and completing  development wells, revenues from producing
             properties,  general and  administrative  costs and operating costs
             will be allocated 15% to the general partner and 85% to the limited
             partners.

2.           SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

             Oil and Gas  Properties - The Company uses the  successful  efforts
             method of  accounting  for its oil and gas  operations.  Under this
             method,  the  costs  of  all  development  wells  are  capitalized.
             Capitalized costs are amortized on the  units-of-production  method
             based on estimated total proved reserves.  The acquisition costs of
             proved oil and gas  properties  are  capitalized  and  periodically
             assessed for impairments.

                                      II-9

<PAGE>




             The Financial  Accounting  Standards Board has issued  Statement of
             Financial   Accounting  Standards  No.  121,  "Accounting  for  the
             Impairment  of Long Lived  Assets and for  Long-Lived  Assets to Be
             Disposed Of." This statement  requires that  long-lived  assets and
             certain  identifiable  intangibles  held and used by the Company be
             reviewed for impairment whenever events or changes in circumstances
             indicate  that  the  carrying   amount  of  an  asset  may  not  be
             recoverable.

             The Company has not determined the effect, if any, on its financial
             position  or  results  of  operations  which  may  result  from the
             adoption of this statement in the first quarter of 1996.

   
             The Company's  operating  interests in oil and gas  properties  are
             recorded  using  the pro  rata  consolidation  method  pursuant  to
             Interpretation 2 of Accounting Principles Board Opinion 18.
    

             Cash Flows - The  Company  has  presented  its cash flows using the
             indirect method and considers all highly liquid investments with an
             original maturity of three months or less to be cash equivalents.

             General and  Administrative  Expenses - The Company  reimburses the
             General Partner for direct costs and administrative  costs incurred
             on its behalf.  Administrative  costs  allocated to the Company are
             computed  on a cost  basis in  accordance  with  standard  industry
             practices  by  allocating  the time spent by the General  Partner's
             personnel  among  all  projects  and by  allocating  rent and other
             overhead on the basis of the relative direct time charges.

             Uses of Estimates - The preparation of the financial  statements in
             conformity with generally accepted  accounting  principles requires
             management  to make  estimates  and  assumptions  that  affect  the
             reported  amounts  of assets  and  liabilities  and  disclosure  of
             contigent  assets  and  liabilities  at the  date of the  financial
             statements and the reported  amounts of revenue and expenses during
             the  reporting  periods.  Actual  results  could  differ from these
             estimates.

3.           FEDERAL INCOME TAXES

             General - The Company is not a taxable  entity for  federal  income
             tax purposes. Such taxes are liabilities of the individual partners
             and the  amounts  thereof  will vary  depending  on the  individual
             situation of each partner.  Accordingly,  there is no provision for
             income taxes in the accompanying financial statements.



                                      II-10

<PAGE>



4.       PAYABLE TO GENERAL PARTNER

         The  payable to  general  partner  primarily  consists  of general  and
         administrative  expenses  allocated  to the  Company by Enex during the
         Company's  start-up phase and for its ongoing  operations.  The Company
         plans to repay the amounts owed to the general partner over a five year
         period.

5.       REPURCHASE OF LIMITED PARTNER INTERESTS

         In accordance  with the partnership  agreement,  the general partner is
         required to purchase  limited  partner  interests (at the option of the
         limited  partners) at annual intervals  beginning after the second year
         following  the  formation  of  the  Company.  The  purchase  price,  as
         specified in the partnership  agreement,  is based primarily on reserve
         reports  prepared by  independent  petroleum  engineers as reduced by a
         specified risk factor.

6.       SIGNIFICANT PURCHASERS

         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.

7.       SALE OF PROPERTY

         Effective October 1, 1995, the Company sold its interest in the Kidd #1
         well in the Enexco  acquisition to Humphrey Oil Co. for $54,600. A gain
         from the sale of $48,589 was recognized by the Company.


                                      II-12

<PAGE>


Item 8.  Changes In and Disagreements With Accountants on Accounting and 
         Financial Disclosure


         Not Applicable


                                     II-14

<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 III -
                                        SERIES 5, L.P.

                                      By:    ENEX RESOURCES CORPORATION
                                              the General Partner



   
December 23, 1996                        By:     /s/   G. B. Eckley
                                              -------------------
                                                       G. B. Eckley, President


                  In  accordance  with the  Exchange  Act,  this report has been
signed below on December 23, 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



                                       S-1