<PAGE>

                                                                  EXHIBIT 10.5

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, PLEDGED, OR
OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT
OR PURSUANT TO RULE 144 OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO
THE CORPORATION AND ITS COUNSEL, THAT SUCH REGISTRATION IS NOT REQUIRED.

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

                          WARRANT to purchase stock

Warrant to Purchase 121,212 Shares of   Issue Date:             November 9, 1999
the Common Stock of Pilot Network       Expiration Date:        November 9, 2004
Services, Inc.                          Initial Exercise Price: $8.25 per share

THIS WARRANT CERTIFIES THAT, for the agreed upon value of $1.00 and for other
good and valuable consideration, GREYROCK CAPITAL, a Division of Banc of America
Commercial Finance Corporation ("Holder") is entitled to purchase the number of
fully paid and non-assessable shares of common stock (the "Shares") of Pilot
Network Services, Inc., a Delaware corporation (the "Company") at the initial
exercise price per Share (the "Warrant Price") all as set forth above and as
adjusted pursuant to Article 2 of this Warrant, subject to the provisions and
upon the terms and conditions set forth in this Warrant.

ARTICLE 1.   EXERCISE.

  1.1   Method of Exercise.  This Warrant is exercisable, in whole or in part,
at any time and from time to time on or before the Expiration Date set forth
above.  Holder may exercise this Warrant by delivering a duly executed Notice of
Exercise in substantially the form attached as Appendix 1 to the principal
office of the Company.  Unless Holder is exercising the conversion right set
forth in Section 1.2, Holder shall also deliver to the Company a check for the
aggregate Warrant Price for the Shares being purchased.

  1.2   Conversion Right.  In lieu of exercising this Warrant as specified in
Section 1.1, Holder may from time to time convert this Warrant, in whole or in
part, into a number of Shares determined by dividing (a) the aggregate fair
market value of the Shares or other securities otherwise issuable upon exercise
of this Warrant minus the aggregate Warrant Price of such Shares by (b) the fair
market value of one Share.  The fair market value of the Shares shall be the
closing price of the Shares (or the closing price of the Company's stock into
which the Shares are convertible) reported for the business day immediately
before Holder delivers its Notice of Exercise to the Company.

  1.3  Delivery of Certificate and New Warrant.  Promptly after Holder exercises
or converts this Warrant, the Company shall deliver to Holder certificates for
the Shares acquired and, if this Warrant has not been fully exercised or
converted and has not expired, a new Warrant representing the Shares not so
acquired.

  1.4   Replacement of Warrants.  On receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Warrant
and, in the case of loss, theft or destruction, on delivery of an indemnity
agreement reasonably satisfactory in form and amount to the Company or, in the
case of mutilation, on surrender and cancellation of this Warrant, the Company
at its expense shall execute and deliver, in lieu of this Warrant, a new warrant
of like tenor.

 1.5   Repurchase on Sale, Merger or Consolidation of the Company.

   1.5.1  "Acquisition".  For the purpose of this Warrant, "Acquisition" means
any sale, license, or other disposition of all or substantially all of the
assets of the Company, or any reorganization, consolidation, or merger of the
Company where the holders of the Company's securities before the transaction
beneficially own less than 50% of the outstanding voting securities of the
surviving entity after the transaction.

   1.5.2   Assumption of Warrant.  If upon the closing of any Acquisition the
successor entity assumes the obligations of this Warrant, then this Warrant
shall be exercisable for the same securities, cash, and property as would be
payable for the Shares issuable upon exercise of the unexercised portion of this
Warrant as if such Shares were outstanding on the record date for the
Acquisition and subsequent closing.  The Warrant Price shall be adjusted
accordingly.

   1.5.3   Nonassumption.  If upon the closing of any Acquisition the successor
entity does not assume the obligations of this Warrant and Holder has not
otherwise exercised this Warrant in full, then the unexercised portion of this
Warrant shall be deemed to have been automatically converted pursuant to Section
1.2 and thereafter Holder shall participate in the acquisition on the same terms
as other holders of the same class of securities of the Company.

ARTICLE 2.   ADJUSTMENTS TO THE SHARES.

  2.1   Stock Dividends, Splits, Etc.  If the Company declares or pays a
dividend on its common stock (or the Shares if the Shares are securities other
than common stock) payable in common stock, or other securities, subdivides the
outstanding common

                                      -1-
<PAGE>

Greyrock Capital                                                      Appendix 1
--------------------------------------------------------------------------------

stock into a greater amount of common stock, or, if the Shares are securities
other than common stock, subdivides the Shares in a transaction that increases
the amount of common stock into which the Shares are convertible, then upon
exercise of this Warrant, for each Share acquired, Holder shall receive,
without cost to Holder, the total number and kind of securities to which
Holder would have been entitled had Holder owned the Shares of record as of
the date the dividend or subdivision occurred.

  2.2   Reclassification, Exchange or Substitution.  Upon any reclassification,
exchange, substitution, or other event that results in a change of the number
and/or class of the securities issuable upon exercise or conversion of this
Warrant, Holder shall be entitled to receive, upon exercise or conversion of
this Warrant, the number and kind of securities and property that Holder would
have received for the Shares if this Warrant had been exercised immediately
before such reclassification, exchange, substitution, or other event.  Such an
event shall include any automatic conversion of the outstanding or issuable
securities of the Company of the same class or series as the Shares to common
stock pursuant to the terms of the Company's Certificate of Incorporation upon
the closing of a registered public offering of the Company's common stock.  The
Company or its successor shall promptly issue to Holder a new Warrant for such
new securities or other property.  The new Warrant shall provide for adjustments
which shall be as nearly equivalent as may be practicable to the adjustments
provided for in this Article 2 including, without limitation, adjustments to the
Warrant Price and to the number of securities or property issuable upon exercise
of the new Warrant.  The provisions of this Section 2.2 shall similarly apply to
successive reclassifications, exchanges, substitutions, or other events.

  2.3   Adjustments for Combinations, Etc.  If the outstanding Shares are
combined or consolidated, by reclassification or otherwise, into a lesser number
of shares, the Warrant Price shall be proportionately increased.

  2.4  No Impairment.  The Company shall not, by amendment of its Certificate of
Incorporation or through a reorganization, transfer of assets, consolidation,
merger, dissolution, issue, or sale of securities or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed under this Warrant by the Company, but shall at all times
in good faith assist in carrying out of all the provisions of this Article 2 and
in taking all such action as may be necessary or appropriate to protect Holder's
rights under this Article against impairment.  If the Company takes any action
affecting the Shares or its common stock other than as described above that
adversely affects Holder's rights under this Warrant, the Warrant Price shall be
adjusted downward and the number of Shares issuable upon exercise of this
Warrant shall be adjusted upward in such a manner that the aggregate Warrant
Price of this Warrant is unchanged.

  2.5   Fractional Shares.  No fractional Shares shall be issuable upon exercise
or conversion of the Warrant and the number of Shares to be issued shall be
rounded down to the nearest whole Share.  If a fractional share interest arises
upon any exercise or conversion of the Warrant, the Company shall eliminate such
fractional share interest by paying Holder an amount computed by multiplying the
fractional interest by the fair market value of a full Share.

  2.6 Certificate as to Adjustments.  Upon each adjustment of the Warrant Price,
the Company at its expense shall promptly compute such adjustment, and furnish
Holder with a certificate of its Chief Financial Officer setting forth such
adjustment and the facts upon which such adjustment is based.  The Company
shall, upon written request, furnish Holder a certificate setting forth the
Warrant Price in effect upon the date thereof and the series of adjustments
leading to such Warrant Price.

ARTICLE 3.    REPRESENTATIONS AND COVENANTS OF THE COMPANY.

  3.1   Representations and Warranties.  The Company hereby represents and
warrants to the Holder as follows:

        (a)  Shares which may be issued upon the exercise of the purchase
right represented by this Warrant shall, upon issuance, be duly authorized,
validly issued, fully paid and non-assessable, and free of any liens and
encumbrances except for restrictions on transfer provided for herein or under
applicable federal and state securities laws.

        (b)  The capitalization of the Company at September 30, 1999 was as
set forth on Schedule 3.1(b) attached hereto, and on the issue date hereof the
Shares shall represent no less than 0.74% of the Company's common stock on a
fully diluted basis.

  3.2   Notice of Certain Events.  If the Company proposes at any time (a) to
declare any dividend or distribution upon its common stock, whether in cash,
property, stock, or other securities and whether or not a regular cash dividend;
(b) to offer for subscription pro rata to the holders of any class or series of
its stock any additional shares of stock of any class or series or other rights;
(c) to effect any reclassification or recapitalization of common stock; (d) to
merge or consolidate with or into any other corporation, or sell, lease,
license, or convey all or substantially all of its assets, or to liquidate,
dissolve or wind up; or (e) offer holders of registration rights the opportunity
to participate in an underwritten public offering of the company's securities
for cash, then, in connection with each such event, the Company shall give
Holder (1) at least 10 business days prior written notice of the date on which a
record will be taken for such dividend, distribution, or subscription rights
(and specifying the date on which the holders of common stock will be entitled
thereto) or for

                                      -2-
<PAGE>

Greyrock Capital                                                      Appendix 1
--------------------------------------------------------------------------------

determining rights to vote, if any, in respect of the matters referred to in
(c) and (d) above; (2) in the case of the matters referred to in (c) and (d)
above, the same notice that is provided to stockholders of the Company
including when the same will take place (and specifying the date on which the
holders of common stock will be entitled to exchange their common stock for
securities or other property deliverable upon the occurrence of such event);
and (3) in the case of the matter referred to in (e) above, the same notice as
is given to the holders of such registration rights.

  3.3   Information Rights.  So long as the Holder holds this Warrant and/or any
of the Shares, the Company shall deliver to the Holder (a) promptly after
mailing, copies of all notices or other written communications to the
shareholders of the Company, (b) unless the Company is subject to and in
compliance with the reporting requirements of the Securities Exchange Act of
1934, as amended (the "Exchange Act"), within ninety (90) days after the end of
each fiscal year of the Company, the annual audited financial statements of the
Company certified by independent public accountants of recognized standing and
(c) unless the Company is subject to and in compliance with the reporting
requirements of the Exchange Act, within forty-five (45) days after the end of
each of the first three quarters of each fiscal year, the Company's quarterly,
unaudited financial statements.

  3.4   Registration Rights.  The Company agrees to use its best efforts to
obtain within sixty days after the date hereof the requisite consent of the
holders of registrable stock under the Company's Existing Rights Agreement (as
defined below) necessary to amend such agreement to grant piggyback registration
rights to Holder with respect to the Shares on the same terms and conditions as
are generally applicable to the other holders of registrable stock thereunder.
For purposes of this Section 3.4, the "Company's Existing Rights Agreement"
shall mean that certain Amended and Restated Investors' Rights Agreement, dated
as of March 31, 1997, among the Company and the investors listed on Schedule I
thereto, as amended by that certain Amendment to Investors' Rights Agreement
dated as of December 22, 1997.

ARTICLE 4.   MISCELLANEOUS.
             -------------

  4.1  This Warrant and the Shares (and the securities issuable, directly or
indirectly, upon conversion of the Shares, if any) shall be imprinted with a
legend in substantially the following form:

  THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED WITHOUT AN
EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT OR PURSUANT TO RULE 144 OR AN
OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE CORPORATION AND ITS COUNSEL
THAT SUCH REGISTRATION IS NOT REQUIRED.

  4.2  Compliance with Securities Laws on Transfer.  This Warrant and the Shares
issuable upon exercise of this Warrant (and the securities issuable, directly or
indirectly, upon conversion of the Shares, if any) may not be transferred or
assigned in whole or in part without compliance with applicable federal and
state securities laws by the transferor and the transferee (including, without
limitation, the delivery of investment representation letters and legal opinions
reasonably satisfactory to the Company, if reasonably requested by the Company).
The Company shall not require Holder to provide an opinion of counsel if the
transfer is to an affiliate of Holder or if there is no material question as to
the availability of current information as referenced in Rule 144(c), Holder
represents that it has complied with Rule 144(d) and (e) the selling broker
represents that it has complied with Rule 144(f), and the Company is provided
with a copy of Holders notice of proposed sale.

  4.3  Transfer Procedure.  Subject to the provisions of Section 4.1 and 4.2,
Holder may transfer all or part of this Warrant or the Shares issuable upon
exercise of this Warrant (or the securities issuable, directly or indirectly,
upon conversion of the Shares, if any) by giving the Company notice of the
portion of the Warrant being transferred setting forth the name, address and
taxpayer identification number of the transferee and surrendering this Warrant
to the Company for reissuance to the transferee(s) (and Holder if applicable).
Unless the Company is filing financial information with the SEC pursuant to the
Exchange Act, the Company shall have the right to refuse to transfer any portion
of this Warrant to any person who directly competes with the Company.

  4.4   Notices.  All notices and other communications from the Company to the
Holder, or vice versa, shall be deemed delivered and effective when given
personally or mailed by first-class registered or certified mail, postage
prepaid, at such address as may have been furnished to the Company or the
Holder, as the case may be, in writing by the Company or such Holder from time
to time.

  4.5  Waiver.  This Warrant and any term hereof may be changed, waived,
discharged or terminated only by an instrument in writing signed by the party
against which enforcement of such change, waiver, discharge or termination is
sought.

  4.6  Attorneys' Fees.  In the event of any dispute between the parties
concerning the terms and provisions of this Warrant, the party prevailing in
such dispute shall be entitled to collect from the other party all costs
incurred in such dispute, including reasonable attorneys' fees.

  4.7  Governing Law.  This Warrant shall be governed by and construed in
accordance with the laws of the State of California, without giving effect to
its principles regarding conflicts of law.

                                      -3-
<PAGE>

Greyrock Capital                                                      Appendix 1
--------------------------------------------------------------------------------

     PILOT NETWORK SERVICES, INC.


     By /s/ M. Marketta Silvera
        -----------------------
        Name: M. Marketta Silvera
        Title:  C.E.O.

                                      -4-
<PAGE>

Greyrock Capital                                                      Appendix 1
--------------------------------------------------------------------------------

                                 Appendix 1
                             NOTICE OF EXERCISE
                             ------------------

  1.  The undersigned hereby elects to purchase ____________ shares of the
Common Stock of Pilot Network Services, Inc. pursuant to the terms of the
attached Warrant, and tenders herewith payment of the purchase price of such
shares in full.

  1.  The undersigned hereby elects to convert the attached Warrant into
Shares/cash [strike one] in the manner specified in the Warrant.  This
conversion is exercised with respect to _______ of the Shares covered by the
Warrant.

 [Strike paragraph that does not apply.]

  2.  Please issue a certificate or certificates representing said shares in the
name of the undersigned or in such other name as is specified below:

                         __________________________
                                   (NAME)

                         __________________________

                         __________________________
                                  (ADDRESS)

  3.  The undersigned represents it is acquiring the shares solely for its own
account and not as a nominee for any other party and not with a view toward the
resale or distribution thereof except in compliance with applicable securities
laws.


_____________________________________
(Signature)

_____________________________________
(Date)

                                      -5-