<PAGE>   1

                                                                    EXHIBIT 10.5

                            ASSIGNMENT OF SECURITIES

         This Assignment of Securities (the "Assignment") is entered into as of
June 26, 2000, by and between HMTF Bridge Teligent, LLC, a Delaware limited
liability company ("Assignor"), and HM4 Teligent Qualified Fund, LLC, a Delaware
limited liability company, HM4 Teligent Private Fund, LLC, a Delaware limited
liability company, HM PG-IV Teligent, LLC, a Delaware limited liability company,
HM 4-SBS Teligent Coinvestors, LLC, a Delaware limited liability company, and HM
4-EQ Teligent Coinvestors, LLC, a Delaware limited liability company
(collectively, the "Assignees").

                                    RECITALS

         A. HMTF-IV Acquisition Corp. entered into that certain Stock Purchase
Agreement, dated as of November 4, 1999 (the "Purchase Agreement"), by and
between Teligent, Inc. (the "Company") and the Purchasers listed on Schedule I
thereto. Capitalized terms not otherwise defined herein shall have the meanings
ascribed to such terms in the Purchase Agreement.

         B. On the terms of the Purchase Agreement, HMTF-IV Acquisition Corp.
agreed to purchase, and the Company agreed to sell, 200,000 shares of the
Company's 7 3/4% Series A Convertible Preferred Stock (the "Purchased
Securities"). Pursuant to that certain Assignment of Rights Under Stock Purchase
Agreement, dated November 9, 1999 (the "Initial Assignment"), HMTF-IV
Acquisition Corp., as assignor, assigned to the Assignees, as assignees, all of
its rights, titles, and interests in, to, and under the Purchase Agreement with
respect to the Purchased Securities.

         C. Pursuant to that certain Assignment of Rights Under Stock Purchase
Agreement, dated November 16, 1999 (the "Second Assignment of Rights"), by and
between Assignees, as assignor, and Assignor, as assignee, the Assignees
assigned to Assignor all of Assignees' rights, titles and interests in, to and
under the Purchase Agreement with respect to 50,000 shares of the Purchased
Securities in the proportions reflected on Exhibit A attached hereto.

         D. Since the Closing, the Company has issued to Assignor an additional
1,923 shares of 7 3/4% Series A Convertible Preferred Stock in dividends as a
result of Assignor's pro rata ownership of its portion of the Purchased
Securities.

         E. Assignor now desires to sell and assign to Assignees all of
Assignor's rights, titles, and interests in, to, and under the Purchase
Agreement with respect to its 51,923 shares of the Company's 7 3/4% Series A
Convertible Preferred Stock in the proportions reflected on Exhibit A attached
hereto.


<PAGE>   2

                                   AGREEMENTS

         NOW, THEREFORE, in consideration of the covenants of Assignees
hereunder and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, intending to
be legally bound, hereby agree as follows:

         1. ASSIGNMENT. Assignor hereby sells, assigns, transfers, and conveys
to each Assignee and its respective successors and assigns the percentage of
Assignor's rights, titles, interests, and obligations in, to, and under the
Purchase Agreement as set forth opposite such Assignee's name on Exhibit A
(including, without limitation, the right to amend, terminate, supplement, and
extend the Purchase Agreement, collectively the "Contract Rights").

         2. ASSUMPTION. Each Assignee hereby agrees to assume and timely perform
all Contract Rights of the Assignor hereby sold, assigned, transferred, and
conveyed to such Assignee. Except as expressly set forth in this Assignment,
Assignees do not hereby assume or agree to pay any other liabilities or
obligations of Assignor of any nature whatsoever.

         3. TITLE TO CONTRACT RIGHTS. Assignor hereby binds itself, its
successors, and assigns to warrant and forever defend, all and singular, title
to the Contract Rights unto Assignees and their respective successors and
assigns against every person lawfully claiming or to claim the same or any part
thereof. Assignor warrants to each Assignee that it is conveying good title to
the Contract Rights free and clear of all Liens.

         4. POWER OF ATTORNEY. Assignor hereby constitutes and appoints each
Assignee as Assignor's true and lawful attorney, with full power of
substitution, for it and in its name, place, and stead, but on behalf of and for
the benefit of such Assignee, to demand and receive from time to time any and
all Contract Rights and to get receipts and releases for and in respect of the
same or any part thereof and to do all and any such acts and things in relation
thereto as such Assignee shall deem advisable.

         5. FURTHER ASSURANCES. Assignor, for itself and its successors and
assigns, hereby covenants and agrees with Assignees that Assignor will do,
execute, acknowledge, and deliver, or will cause to be done, executed,
acknowledged, and delivered, all such further acts, conveyances, transfers,
assignments, powers of attorney, and assurances that may be required to assure,
convey, transfer, confirm, and vest unto Assignees any and all of the Contract
Rights and to aid and assist Assignees in collecting and reducing the Contract
Rights to possession.

         6. GOVERNING LAW. This Assignment shall be governed by and construed in
accordance with the laws of the State of New York.


               [THE REMAINDER OF THIS PAGE IS INTENTIONALLY BLANK]




                                       2
<PAGE>   3

         IN WITNESS WHEREOF, the undersigned have caused this Agreement to be
signed, all as of the date first written above.

                                   ASSIGNOR:

                                   HMTF BRIDGE TELIGENT, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------


                                   ASSIGNEES:

                                   HM4 TELIGENT QUALIFIED FUND, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------




                                   HM4 TELIGENT PRIVATE FUND, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------


                                   HM PG-IV TELIGENT, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------


                  [SIGNATURE PAGE TO ASSIGNMENT OF SECURITIES]

                                       S-1


<PAGE>   4






                                   HM 4-SBS TELIGENT COINVESTORS, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------




                                   HM 4-EQ TELIGENT COINVESTORS, LLC



                                   By: /s/ David W. Knickel
                                      ------------------------------------------
                                   Name: David W. Knickel
                                         ---------------------------------------
                                   Title: Vice President
                                         ---------------------------------------



<PAGE>   5


                                    EXHIBIT A

                            ASSIGNMENT OF SECURITIES


<TABLE>
<CAPTION>
                                                                            SHARES OF SERIES A
                                                                             7.5% CONVERTIBLE
                                                           PERCENTAGE        PREFERRED STOCK
                     ASSIGNEE                              TRANSFERRED        TO BE ACQUIRED
                     --------                              -----------      ------------------

<S>                                                        <C>              <C>
HM4 Teligent Qualified Fund, LLC                           90.805306%             47,149
HM4 Teligent Private Fund, LLC                              0.643298%                334
HM PG-IV Teligent, LLC                                      4.834331%              2,510
HM 4-SBS Teligent Coinvestors, LLC                          2.232843%              1,159
HM 4-EQ Teligent Coinvestors, LLC                           1.484222%                771
Total                                                       100.0000%             51,923
</TABLE>