The Evasion jailbreak for iPhones running iOS 6.x was patched up real well by Apple in iOS 6.1.3. But a dev has managed to finally crack version 6.1.4 on the iPhone 5.
iOS 6.1.4 rolled out in May for iPhone 5 users, offering bug fixes and stymying jailbreaks. But developer Wincom now has iOS 6.1.4 running Cydia on an iPhone 5. Details are pretty thin on the ground, but Wincom has at least uploaded some of the code required to make the jailbreak work for iOS 6.1.4, and forums seem to suggest that some people have successfully managed to use it.
Sadly, it's quite an involved process: you'll need to wrangle with your own kernel exploits as well as using Wincom's code to jailbreak your iPhone 5 with iOS 6.1.4. One for the more technically minded then. [Redmond Pie - Thanks George!]