A group of iOS hackers called Evad3rs released the first untethered jailbreak for your iPhone 5, and most other iOS 6.0 or 6.1 devices. According to CNET, The evasi0n tool, as it's called, allows users to install applications available outside Apple's AppStore through alternatives like Cydia.
You can run the evasi0n jailbreak on Mac, Windows and Linus software. Here's a list of the devices it will work on (via Gizmodo):
iPod touch 4th generation
iPod touch 5th generation
Apple released its latest iOS platform, iOS 6.1, just one week ago.