<PAGE>
 
                                                                    EXHIBIT 10.5

                     NON-QUALIFIED STOCK OPTION AGREEMENT
                                   under the
                                  ACSYS, INC.
                  AMENDED AND RESTATED 1997 STOCK OPTION PLAN


          Optionee:       Brady W. Mullinax, Jr.
                   --------------------------------------------- 

          Number Shares Subject to Option:            123,563
                                          ----------------------
 
          Exercise Price per Share:                  $ 11.125
                                   -----------------------------
 
          Date of Grant:                      August 21, 1998
                        ----------------------------------------
 
     1.   Grant of Option.  Acsys, Inc. (the "Company") hereby grants to the
          ---------------                                                   
Optionee named above (the "Optionee"), under the Acsys, Inc. Amended and
Restated 1997 Stock Option Plan (the "Plan"), an Non-Qualified Stock Option to
purchase, on the terms and conditions set forth in this agreement (this "Option
Agreement"), the number of shares indicated above of the Company's common stock
(the "Stock"), at the exercise price per share set forth above (the "Option").
Capitalized terms used herein and not otherwise defined shall have the meanings
assigned such terms in the Plan.

     2.   Vesting of Option.
          ----------------- 

          (a)  Normal Vesting.  Unless the exercisability of the Option is
               --------------                                             
accelerated in accordance with Section (b) below or otherwise, the Option shall
vest (become exercisable) in accordance with the following schedule:

<TABLE>
<CAPTION>
                                                  Number of Option
                                                  ----------------
               Date                                Shares Vested
               ----                                -------------
         <S>                                      <C>  
         Date of Grant                               16,298.82     
                                                                   
         December 31, 1998                           24,712.60     
                                                                   
         December 31, 1999                           41,275.79     
                                                                   
         December 31, 2000                           41,275.79      
                                                                              
</TABLE>

[ ]

          (b)  Change in Control.  In the event of a Change in Control (as
               -----------------                                          
defined in Optionee's Employment Agreement), the Option shall become immediately
exercisable in 
<PAGE>
 
full.

[ ]

[ ] 

          (c)  Certain Terminations.  In the event Optionee's employment with
               --------------------                                          
the Company is terminated by the Company without Cause (as defined in Optionee's
Employment Agreement) or by Optionee for Good Reason (as defined in Optionee's
Employment Agreement), the Option shall become immediately exercisable in full.

     3.   Period of Option and Limitations on Right to Exercise.  The Option
          -----------------------------------------------------             
will, to the extent not previously exercised, lapse under the earliest of the
following circumstances; provided, however, that the Committee may, prior to the
lapse of the Option under the circumstances described in paragraphs (b), (c) and
(d) below, provide in writing that the Option will extend until a later date:

          (a)  The Option shall lapse as of 5:00 p.m., Eastern Time, on the
     tenth anniversary of the date of grant (the "Expiration Date").

          (b)  The Option shall lapse three months after Optionee's termination
     of employment for any reason other than Optionee's death or Permanent and
     Total Disability.
 
          (c)  In the event of termination of employment because of Optionee's
     Permanent and Total Disability, the Option shall lapse one year after the
     date of the Optionee's termination of employment.
 
          (d)  If the Optionee dies while employed by the Company or any of its
     Subsidiaries, or during the three-month period described in subsection (b)
     above, or during the one-year period described in subsection (c) above, and
     before the Option otherwise lapses, the Option shall lapse one year after
     the date of the Optionee's death.  Upon the Optionee's death, the Option
     may be exercised by the Optionee's beneficiary.

     If the Optionee or his beneficiary exercises an Option after termination of
employment, the Option may be exercised only with respect to the shares that
were otherwise vested on the Optionee's termination of employment.

     4.   Exercise of Option.  The Option shall be exercised by written notice
          ------------------                                                  
directed to the Secretary of the Company at the principal executive offices of
the Company, in substantially the form attached hereto as Exhibit A, or such
other form as the Committee may approve.  Such written notice shall be
accompanied by full payment in cash, shares of Stock previously acquired by the
Optionee, or any combination thereof, for the number of shares specified in such
written notice; provided, however, that if shares of Stock are used to pay the
exercise price, such shares must have been held by the Optionee for at least six
months.  The Fair Market Value of the surrendered Stock as of the date of 

                                      -2-
<PAGE>
 
the exercise shall be determined in valuing Stock used in payment of the
exercise price. To the extent permitted under Regulation T of the Federal
Reserve Board, and subject to applicable securities laws, the Option may be
exercised through a broker in a so-called "cashless exercise" whereby the broker
sells the Option shares and delivers cash sales proceeds to the Company in
payment of the exercise price.

     Optionee must exercise the Option for at least the lesser of 100 shares or
the number of shares of Purchasable Stock as to which the Option remains
unexercised.  Subject to the terms of this Option Agreement, the Option may be
exercised at any time and without regard to any other option held by the
Optionee to purchase stock of the Company.

     5.   Limitation of Rights.  The Option does not confer to the Optionee or
          --------------------                                                
the Optionee's personal representative any rights of a shareholder of the
Company unless and until shares of Stock are in fact issued to such person in
connection with the exercise of the Option.  Nothing in this Option Agreement
shall interfere with or limit in any way the right of the Company or any
Subsidiary to terminate the Optionee's employment at any time, nor confer upon
the Optionee any right to continue in the employ of the Company or any
Subsidiary.

     6.   Stock Reserve.  The Company shall at all times during the term of this
          -------------                                                         
Option Agreement reserve and keep available such number of shares of Stock as
will be sufficient to satisfy the requirements of this Option Agreement.

     7.   Optionee's Covenant.  The Optionee hereby agrees to use his best
          -------------------                                             
efforts to provide services to the Company in a workmanlike manner and to
promote the Company's interests.

     8.   Restrictions on Transfer and Pledge.  The Option may not be pledged,
          -----------------------------------                                 
encumbered, or hypothecated to or in favor of any party other than the Company
or a Parent or Subsidiary, or be subject to any lien, obligation, or liability
of the Optionee to any other party other than the Company or a Parent or
Subsidiary.  The Option is not assignable or transferable by the Optionee other
than by will or the laws of descent and distribution or pursuant to a Qualified
Domestic Relations Order.  The Option may be exercised during the lifetime of
the Optionee only by the Optionee (or by Optionee's guardian or legal
representative, should one be appointed).

     9.   Plan Controls.  The terms contained in the Plan are incorporated into
          -------------                                                        
and made a part of this Option Agreement and this Option Agreement shall be
governed by and construed in accordance with the Plan.  In the event of any
actual or alleged conflict between the provisions of the Plan and the provisions
of this Option Agreement, the provisions of the Plan shall be controlling and
determinative.

     10.  Successors.  This Option Agreement shall be binding upon any successor
          ----------                                                            
of the Company, in accordance with the terms of this Option Agreement and the
Plan.

                                      -3-
<PAGE>
 
     11.  Severability.  If any one or more of the provisions contained in this
          ------------                                                         
Option Agreement are invalid, illegal or unenforceable, the other provisions of
this Option Agreement will be construed and enforced as if the invalid, illegal
or unenforceable provision had never been included.

     12.  Notice.  Notices and communications under this Option Agreement must
          ------                                                              
be in writing and either personally delivered or sent by registered or certified
United States mail, return receipt requested, postage prepaid.  Notices to the
Company must be addressed to:

          Acsys, Inc.
          75 14th Street
          Atlanta, Georgia 30309
          Attn: Secretary

or any other address designated by the Company in a written notice to the
Optionee.  Notices to the Optionee will be directed to the address of the
Optionee then currently on file with the Company, or at any other address given
by the Optionee in a written notice to the Company.

     13.  Binding Agreement.  This Agreement shall be binding upon the parties
          -----------------                                                   
hereto and their representatives, successors and assigns.

     14.  Governing Law.  This Agreement is executed and delivered in, and shall
          -------------                                                         
be governed by the laws of, the State of Georgia.

     15.  Amendments.  This Agreement may not be modified except in a writing
          ----------                                                         
executed by each of the parties hereto.

                                      -4-
<PAGE>
 
     IN WITNESS WHEREOF, Acsys, Inc., acting by and through its duly authorized
officers, has caused this Option Agreement to be executed, and the Optionee has
executed this Option Agreement, all as of the day and year first above written.


                              ACSYS, INC.


                              By: /s/ Timothy Mann, Jr.
                                  ------------------------------------------
                              Name: Timothy Mann, Jr.

                              Title: President and Chief Executive Officer



                              OPTIONEE:

                                    /s/ Brady W. Mullinax, Jr.
                              ----------------------------------------------
                                        Brady W. Mullinax, Jr.

                              Address:


                                  116 Huntington Road
                              ----------------------------------------------
                                  Atlanta, GA 30307
                              ----------------------------------------------

                                      -5-
<PAGE>
 
                                      [ ]   
 
                                   EXHIBIT A
                                   ---------

                   NOTICE OF EXERCISE OF OPTION TO PURCHASE
                                COMMON STOCK OF
                                  ACSYS, INC.


                              Name:

                              _________________________________
                              Address:

                              _________________________________
                              _________________________________

                              Date: ___________________________


Acsys, Inc.
75 14th Street
Atlanta, Georgia 30309
Attn: Secretary

Re:  Exercise of Non-Qualified Stock Option

     I elect to purchase ______________ shares of Common Stock of Acsys, Inc.
pursuant to the Acsys, Inc. Non-Qualified Stock Option Agreement dated
______________ and the Acsys, Inc. Amended and Restated 1997 Stock Option Plan.
The purchase will take place on the Exercise Date, which will be as soon as
practicable following the date this notice and all other necessary forms and
payments are received by the Company, unless I specify a later date (not to
exceed 30 days following the date of this notice).

     On or before the Exercise Date, I will pay the full exercise price in the
form specified below (check one):

     [ ]  Cash Only: by delivering a certified or a cashier's check to Acsys, 
          --------- 
          Inc. for $___________.

     [ ]  Cash and Shares: by delivering a certified or a cashier's check to 
          ---------------
          Acsys, Inc. for $_________ for the part of the exercise price. I will
          pay the balance of the exercise price by delivering to the Company a
          stock certificate with my endorsement for shares of Acsys Stock that I
          have 
<PAGE>
 
          owned for at least six months. If the number of shares of Acsys
          Stock represented by such stock certificate exceeds the number needed
          to pay the exercise price (based on the Fair Market Value of the Acsys
          Stock on the date of delivery), the Company will issue me a new stock
          certificate for the excess.

     [ ]  Shares Only: by delivering to the Company a stock certificate with my
          -----------                                                          
          endorsement for shares of Acsys Stock that I have owned for at least
          six months.  If the number of shares of Acsys Stock represented by
          such stock certificate exceeds the number needed to pay the exercise
          price (based on the Fair Market Value of the Acsys Stock on the date
          of delivery), the Company will issue me a new stock certificate for
          the excess.

     [ ]  Cash From Broker: by delivering the purchase price from
          ----------------                                       
          _______________________, a broker, dealer or other "creditor" as
          defined by Regulation T issued by the Board of Governors of the
          Federal Reserve System (the "Broker").  I authorize the Company to
          issue a stock certificate in the number of shares indicated above in
          the name of the Broker in accordance with instructions received by the
          Company from the Broker and to deliver such stock certificate directly
          to the Broker (or to any other party specified in the instructions
          from the Broker) upon receiving the exercise price from the Broker.

     Please deliver the stock certificate to me (unless I have chosen to pay the
     purchase price through a broker).

                              Very truly yours,

                              ________________________

AGREED TO AND ACCEPTED:

ACSYS, INC.

By: _____________________________________

Title: __________________________________

Number of Option Shares
Exercised: ______________________________

Number of Option Shares
Remaining: ______________________________

Date: ___________________________________

                                      -2-