Supplemental Agreement No. 1 to Purchase Agreement No. 03776 between The Boeing Company and UnitedContinental Holdings, Inc. Relating to Boeing Model 737-9 Aircraft

Exhibit 10.5

Supplemental Agreement No. 1

to

Purchase Agreement No. 03776

between

The Boeing Company

and

United Continental Holdings, Inc.

Relating to Boeing Model 737-9 Aircraft

THIS SUPPLEMENTAL AGREEMENT, entered into as of June 17, 2013, by and between THE BOEING COMPANY (Boeing) and UNITED CONTINENTAL HOLDINGS, INC. (Customer);

WHEREAS, the parties hereto entered into Purchase Agreement No. 03776 dated July 12, 2012, as amended and supplemented (the Purchase Agreement), relating to the purchase and sale of Boeing Model 737-9 aircraft (Aircraft). This Supplemental Agreement is an amendment to the Purchase Agreement;

WHEREAS, Boeing and Customer have agreed to *** Aircraft *** scheduled for delivery from *** through *** (MAX *** Aircraft);

WHEREAS, Boeing and Customer agree that 787-10 Model aircraft program launch requires approval from the Boeing Board of Directors, pursuant to Letter Agreement as detailed in Letter Agreement UAL-PA-03860-LA-1301380.

WHEREAS, Boeing and Customer agree that the MAX *** Aircraft will be ***;

NOW THEREFORE, in consideration of the mutual covenants herein contained, the parties agree to amend the Purchase Agreement as follows:

1. Table of Contents and Tables:

1.1 Remove and replace, in its entirety, the “Table of Contents,” with the “Table of Contents” attached hereto, to reflect the changes made by this Supplemental Agreement No. 1.

CONFIDENTIAL MATERIAL APPEARING IN THIS DOCUMENT HAS BEEN OMITTED AND FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION IN ACCORDANCE WITH THE SECURITIES ACT OF 1933, AS AMENDED, AND RULE 24B-2 PROMULGATED THEREUNDER. OMITTED INFORMATION HAS BEEN REPLACED WITH ASTERISKS.

1.2 Remove and replace, in its entirety, Table 1 for the Aircraft with the Table 1 attached hereto and marked with the “SA-1” legend.

2. Effective Date:

This Supplemental Agreement No. 1 shall be effective subject to satisfaction of all of the following conditions precedent (collectively the Conditions Precedent):

Execution of Supplemental Agreement No. 1 to Purchase Agreement No. 3860 between Boeing and United Airlines, Inc. (United) relating to Model 787 aircraft (the UAL Purchase Agreement) by Boeing and United;

Execution of Supplemental Agreement No. 8 to Purchase Agreement No. 2484 (the CAL Purchase Agreement) between Boeing and United relating to Boeing Model 787 aircraft by Boeing and United;

Execution of this Supplemental Agreement No. 1 to the Purchase Agreement;

Upon satisfaction of the Conditions Precedent, the Agreement will be deemed to be supplemented to the extent herein provided as of the date hereof and as so supplemented will continue in full force and effect.

[The rest of the page is intentionally blank. Signature page follows.]

EXECUTED IN DUPLICATE as of the day and year first written above.

TABLE OF CONTENTS

TABLE OF CONTENTS, CONTINUED

Table 1 To

Purchase Agreement No. 03776

737-9 Aircraft Delivery, Description, Price and Advance Payments

Table 1 To

Purchase Agreement No. 03776

737-9 Aircraft Delivery, Description, Price and Advance Payments

Table 1 To

Purchase Agreement No. 03776

737-9 Aircraft Delivery, Description, Price and Advance Payments

Table 1 To

Purchase Agreement No. 03776

737-9 Aircraft Delivery, Description, Price and Advance Payments