I had the exact same clicking issue with my 5S went to apple store (made genius bar appointment prior) tech looked at my iphone for 10 seconds left and came back with replacement.
Below this is the work order.
Thank you for visiting the Apple Store. Below is a copy of your service record.
Apple Store West Edmonton
28-Sep-13
(780) 701-0540
Genius Bar Work Authorization
Repair No: R104002348
Customer Information
Product Information
Warranty Status: In Warranty(LP) Model: IPHONE 5S
Date of Purchase: 20-Sep-13
Serial No: DNPLC0AEFFFV
Problem Description/Diagnosis
Issue: Home button clicks loudly.
Steps to Reproduce: Tested button.
Cosmetic Condition: New.
Employee 1124302564
Repair Estimate
Item Number Description Price Amount Due
661-7721 SVC IPHONE 5S GSM 64GB GOLD CI/AR $ 0.00 $ 0.00
S5140Z/A IPHONE 5S FLAT RATE REPAIR RETAIL-INT $ 269.00 $ 0.00
Tax $ 0.00
Total $ 269.00 $ 0.00
I agree that:
• the Repair Terms and Conditions on the reverse side of this page will apply to the service of the product identified above;
• Apple is not responsible for any loss, corruption, or breach of the data on my product during service; and
• as loss of data may occur as a result of the service, it is my responsibility to make a backup copy of my data before bringing my product to Apple for service;
• goods presented for repair may be replaced by refurbished goods of the same type rather than being repaired. Refurbished parts may be used to repair the goods
Repair Terms and Conditions can be found at http://www.apple.com/legal/terms/repair/instantexchange.html.