Apple has done a much better job of letting you to activate and update your iphone without using wires and that sound true for the iPhone 5. To download and install iOS 6.1 on your iPhone 5, simple way go into your Settings and then tap on Software Update. Hit the Download and Install button and then you will have to agree to the Terms and Conditions.
From there, your iPhone 5 will download the update and we suggest that you keep your phone plugged in a power sources and download the update over WiFi so that data will not go against your monthly data cap. Once it is downloaded, just follow the onscreen instructions and in about 10 to 15 minutes, you will have iOS 6.1 on your iPhone 5.
If you want to update using your computer you can hook up your iPhone 5 to your Mac or PC and then launch iTunes. Click on the iPhone 5 icon and then go to the Summary page. From there, click on Check for Update and follow the onscreen instructions.
The update should take about 10 to 15 minutes to download and install. Be sure that your iPhone 5 has more than 25 percent battery life before you try to update to iOS 6.1.
