Exhibit (a)(5)

Southwest Airlines Co. Announces Fundamental Change, Right to Convert, and Redemption Notification for 7% Convertible Notes Due 2023

Dallas, May 4, 2011—Southwest Airlines Co. (NYSE: LUV) announced today that it is notifying holders of the $5,472,000 outstanding principal amount of its 7% Convertible Notes due 2023 (the “Notes”) that they have an option, pursuant to the terms of the Notes, to require Southwest to purchase, on June 6, 2011, all or a portion of such holders’ Notes (the “Redemption Option”) for cash at a price equal to $1,000 per $1,000 principal amount of the Notes, plus any accrued and unpaid interest to, but not including, June 6, 2011.

Southwest is also notifying holders of the Notes that a Fundamental Change, as defined in the Indenture governing the Notes, occurred on May 2, 2011 in connection with the closing of the acquisition of AirTran Holdings, Inc., pursuant to the Agreement and Plan of Merger, dated as of September 26, 2010, by and among Southwest, AirTran Holdings, Inc., and Guadalupe Holdings Corporation.

Finally, Southwest is notifying holders of the Notes that it will redeem all outstanding Notes on June 21, 2011 at a redemption price in cash equal to $1,000 per $1,000 principal amount of the Notes, plus any accrued and unpaid interest to, but not including, June 21, 2011.

As required by rules of the Securities and Exchange Commission, Southwest will file a Tender Offer Statement on Schedule TO later today. In addition, Southwest’s company notice to holders (a copy of which will be attached as an exhibit to such Schedule TO) with respect to the matters described above will be available through The Depository Trust Company and the paying agent, which is Wilmington Trust Company. None of Southwest, its board of directors, or its employees has made or is making any representation or recommendation to any holder as to whether to exercise or refrain from exercising the Redemption Option.

Noteholders’ opportunity to exercise the Redemption Option will commence on May 4, 2011, and will terminate at 5:00 p.m. EST, on June 6, 2011. Holders may withdraw any previously delivered purchase notice pursuant to the terms of the Redemption Option at any time prior to 5:00 p.m. EST, on June 6, 2011.

The address of Wilmington Trust Company is set forth in the company notice to holders.

This press release is for informational purposes only and is not an offer to purchase, or the solicitation of an offer to purchase, the Notes.

About Southwest Airlines Co.

In its 40th year of service, Southwest Airlines continues to differentiate itself from other low-fare carriers—offering a reliable product with exemplary Customer Service. Southwest Airlines is the nation's largest carrier in terms of originating domestic passengers boarded, now serving 72 cities in 37 states with the addition of service to Newark Liberty International Airport on March 27, 2011. Southwest also is one of the most honored airlines in the world known for its commitment to the triple bottom line of Performance, People, and Planet. To read more about how Southwest is doing its part to be a good citizen, visit southwest.com/cares to read the Southwest Airlines One Report(TM). Based in Dallas, Southwest currently operates more than 3,400 flights a day and has more than 35,000 Employees systemwide.