FIVE9, INC. AMENDMENT TO OFFER LETTER

Exhibit 10.4

October 20, 2009

Mr. Dan Burkland

Dear Dan:

We are very pleased to offer you employment with Five 9, Inc. (“Company” or “Five9”) for the position of Senior Vice President of Sales. In this position you will report to Mike Burkland, Chief Executive Officer. This is an exempt position, which carries considerable responsibility and which is integral to the continued development and success of our Company. This letter formally presents the specifics of our offer of employment, which you should read and carefully consider.

In this position, beginning on or about December 7, 2009 you will receive an annual base salary of $200,000, paid bi-monthly at a rate of $8,333.33 per pay period. Additionally, beginning on January 1, 2010 you will be eligible to earn a Quarterly Commission Bonus which is targeted at $31,250 per quarter, with the actual amount paid based upon the attainment of your specific sales objectives as set by the Company. In the case you over achieve these sales objectives, the Quarterly Commission Bonus will be limited to $62,500 per quarter. For the first 90 days of your employment your Quarterly Commission Bonus will be guaranteed to be at least $31,250. For the second 90 days of your employment your Quarterly Commission Bonus will be guaranteed to be at least $15,625. Payment of each Quarterly Commission Bonus requires that you are an employee in good standing at the end of each Quarterly period.

You will also be given a signing bonus equal to $30,000 which will be paid in three (3) equal installments of $10,000 each at the end of January 2010, February 2010 and March 2010. Payment of each installment requires that you are an employee in good standing at the end of each installment period.

Of course, all of the previously discussed compensation will be subject to standard payroll deductions and withholdings.

The Company has adopted an Equity Incentive Plan (the “Stock Option Plan”). Subject to approval by the Board of Directors, Company will grant you a nonqualified stock option (the “Initial Option”) to purchase 1,507,607 shares of the Company’s common stock at a price per share equal to the fair market value of a share of the Company’s common stock on the date of the option grant as determined by the Board of Directors of Five9, Inc. The Initial Option will vest with respect to twenty-five percent (25%) of the shares subject to the Initial Option on the first anniversary of your start date. The

Five 9, Inc. — 7901 Stoneridge Dr. Suite 200, Pleasanton, CA 94588 — 925 ###-###-#### — www.five9.com

remaining seventy-five percent (75%) of the shares subject to the Initial Option will vest in thirty-six (36) substantially equal monthly installments thereafter. In each case, the vesting of the Initial Option is subject to your continued services to the Company through the respective vesting date.

Change in Control. If a Change in Control of the Company (as defined below) occurs and more than fifty percent (50%) of the Option is then outstanding and unvested, the vesting of the Option shall accelerate such that (after giving effect to such acceleration and taking into account any portion of the Option that had theretofore become vested and exercisable), the Option shall have become vested and exercisable as of the Change in Control date with respect to fifty percent (50%) of the total number of shares subject to the original Option grant. In addition, if your employment is terminated by the Company other than for Cause or due to Constructive Termination at any time within a period of twelve (12) months following a Change in Control of the Company, then (i) the Option, to the extent outstanding and unvested (after giving effect to the accelerated vesting contemplated above), shall immediately become vested and exercisable with respect to fifty percent (50%) of the shares covered by the then-outstanding and unvested portion. Any portion of the Option that is not vested after giving effect to the foregoing clause (i) shall terminate as of the date of such termination of your employment.

For purposes of this Agreement, “Change in Control” shall mean the occurrence of any of the following on or after the Effective Date:

In the event you are terminated, without Cause, after the 180th day of employment with the Company, you will be entitled to receive a severance equal to 6 months of your then-current base salary and benefits (subject to standard withholding and payroll deductions), payable in accordance with the Company’s customary payroll practices.

Five 9, Inc. — 7901 Stoneridge Dr. Suite 200, Pleasanton, CA 94588 — 925 ###-###-#### — www.five9.com

You will be entitled to 15 days of Paid Time-Off (PTO) per year. Your PTO will accrue at the rate of 1.25 days per month. As a full-time employee of the Company, you will be eligible to participate in Company-sponsored benefits and be a member of any employee benefit plans that the Company may establish and that are generally available to other employees of the Company. At the present time, these benefits include medical, dental and vision. In the near future, we will provide you more detailed information about these benefits, including eligibility rules.

Employment at the Company is “at will.” This means that you are free to resign at any time with or without Cause (defined below) or prior notice. Similarly, the Company is free to terminate our employment relationship with you at any time, with or without Cause or prior notice. As you know, Five9 is involved in a highly competitive and quickly evolving industry. Although your job duties, title, compensation and benefits, as well as the Company’s policies and procedures, may change from time-to-time, the “at-will” nature of your employment may only be changed in a document signed by you and the CEO of the Company. Your employment with the Company is subject to Five9’s general employment policies, many of which are described in the Five9 Employee Handbook.

You will devote your best efforts to the performance of your job for Company. While employed at Company, you will not undertake any other activity requiring your business time and attention, nor support (by way of investment or otherwise) any activity that may be competitive with the Company’s business or pose a conflict of interest with that business. You will follow the Company’s polices and procedures (including our policies protecting other employees against discrimination and sexual harassment) as described to you from time to time.

Your employment pursuant to this offer is contingent on the following: (1) your signing of the Company’s Proprietary Information and Inventions Assignment Agreement, which, among other things, requires that you will not, during your employment with the Company, improperly use or disclose any proprietary information or trade secrets of any former employer and will not bring onto the Company’s premises any confidential or proprietary information of any former employer unless that employer has consented to such action in writing; (2) your ability to provide the Company with the legally-required proof of your identity and authorization to work in the United States; (3) our satisfaction that you will not be in violation of any non-compete, proprietary invention and information agreements, or any other similar agreement between you and any current or former employer; and (4) completion of satisfactory reference checking.

Five 9, Inc. — 7901 Stoneridge Dr. Suite 200, Pleasanton, CA 94588 — 925 ###-###-#### — www.five9.com

In the unlikely event of a dispute between Company and you arising out of your employment or the termination of your employment, we each agree to submit our dispute to binding arbitration in the City and County of Alameda, California. This means that there will be no court or jury trial of disputes between us concerning your employment or the termination of your employment. While this agreement to arbitrate is intended to be broad (and covers, for example, claims under state and federal laws prohibiting discrimination on the basis of race, sex, age, disability, family leave, etc.), it is not applicable to your rights under the California Workers’ Compensation Law, which are governed under the special provisions of that law, or to enforcement of the attached agreement concerning confidential information and ownership of inventions.

Dan, we hope that you will accept our employment offer on the above terms and conditions, which can be modified only in a writing signed by the Company’s Chief Executive Officer. This letter sets forth the terms of your employment with us and supersedes any prior representations or agreements, whether written or oral. We realize that this sounds a bit formal, but we want to make sure that you understand the important aspects of employment at Five9, before you make a decision about joining us. To accept our offer, please return one original copy of your signed offer letter to me at your earliest convenience.

Please contact me if you have any questions whatsoever about this letter or your employment. We are looking forward to you joining us as a member of the Five9 team.

Five 9, Inc. — 7901 Stoneridge Dr. Suite 200, Pleasanton, CA 94588 — 925 ###-###-#### — www.five9.com

FIVE9, INC.

AMENDMENT TO OFFER LETTER

THIS AMENDMENT TO OFFER LETTER (this “Amendment”) by and between Five9, Inc., a Delaware corporation (the “Company”), and Dan Burkland (“Executive” or “you”) is made effective as of March 19, 2012 (the “Effective Date”) under the terms and subject to the provisions provided below.

In consideration of the terms and conditions set forth below and Executive’s continued employment with the Company, Executive and the Company agree to amend the Employment Offer Letter, dated October 20, 2009, between Executive and the Company, attached hereto as Exhibit A (“Offer Letter”) as follows:

1. Cause. For purposes of the Offer Letter, “Cause” shall mean (i) fraud, embezzlement, willful misconduct or a material violation of law that is materially detrimental to the Company or any of its affiliates; (ii) gross negligence with respect to the Company or any of its affiliates that causes material harm to the Company or any affiliate; (iii) conviction or plea of guilty or nolo contendere for a felony or a crime of moral turpitude that causes material harm to the Company’s reputation or (iv) a material breach of any provision of this Offer Letter or any provision of the Company’s Code of Conduct that is applicable to the Company’s employees; provided, however, that if a cure is reasonably possible in the circumstances, that at least 15 days’ advance written notice of such breach has been provided (which notice shall specifically set forth the nature of such breach), and failure to cure such breach within such 15-day period.

2. Constructive Termination. For purposes of this Offer Letter, “Constructive Termination” shall mean a material default by the Company in the performance of its obligations hereunder, provided such default shall not have been corrected by the Company within 30 days of receipt by the Company of written notice from you of the occurrence of such default, which notice shall specifically set forth the nature of such default. Material default under this Offer Letter shall include, without limitation, (i) the assignment to you of any duties inconsistent (except in the nature of a promotion) with your position as Senior Vice President of Sales of the Company or a material adverse alteration in the nature or status of your responsibilities, (ii) the Company’s failure to pay any of the compensation that has become due and payable to you hereunder, and (iii) a relocation by the Company of your principal office more than thirty-five (35) miles from Pleasanton, California that occurs without your prior written consent.

3. Severance. In the event your employment is terminated by the Company, without Cause, or by you pursuant to a Constructive Termination, you will be entitled to receive severance equal to 6 months base salary (subject to standard withholding and payroll deductions), payable in installments in accordance with the Company’s customary payroll practices. During the period in which you are paid a severance from the Company, the Company will pay for the continuation of your health benefits.

4. Acknowledgement and Waiver. Executive and the Company hereby acknowledge that Executive shall not be entitled to receive the severance benefits provided for in the Offer Letter unless the Executive signs and does not revoke a general release of claims in the form provided by the Company.

5. Other Terms. All other terms and conditions in the Offer Letter shall remain unchanged.

6. Miscellaneous.

D. Executive’s Acknowledgements. Executive acknowledges that Executive: (a) has read this Amendment; (b) has been represented in the preparation, negotiation, and execution of this Amendment by legal counsel of Executive’s own choice or has voluntarily declined to seek such counsel; (c) understands the terms and consequences of this Amendment; (d) understands that this Amendment does not constitute a contract of employment or obligate the Company to retain Executive as an employee; and (e) understands that the law firm of Jones Day is acting as counsel to the Company in connection with the transactions contemplated by this Amendment, and is not acting as counsel for Executive.

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IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the day and year first set forth above.

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EXHIBIT A

OFFER LETTER