It appears that chpwn has already jailbroken the iPhone 5!
This tweet was posted by chpwn, a popular jailbreak developer moments ago. The picture shows an iPhone 5 running iOS 6 with Cydia installed.
Taller screens like Cydia too. :) pic.twitter.com/fE14vXN2
We've also independently confirmed that the iPhone 5 is indeed jailbroken. We don't know any further information or whether the jailbreak will be released publicly.
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Chpwn has posted a photo of Cydia running on the iPhone 5.