Apple iPhone 5

iOS 7.1 - Untethered Jailbreak - VIDEO
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http://evasi0n-jailbreak.net
To everyone’s surprise, the evad3rs team today released evasi0n jailbreak for iPhone, iPod touch and the iPad. evasi0n is an untethered jailbreak for devices running iOS 7.x.x through iOS 7.1.
YES! iOS 7.1 is supported!
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Go to: http://evasi0n-jailbreak.net
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evasi0n is available for Mac and Windows, and is untethered. Here are the requirements posted on the evasi0n website:

5 minutes of your time!
A computer, running Windows (XP minimum), Mac OS X (10.6 minimum) or Linux (x86 / x86_64)
iTunes installed if you’re running Windows
An iPhone, iPad or iPod running iOS 7.0 through 7.1 (you may check in Settings / General / About => Version)
A USB cable to connect the device to the computer