You will soon be able to jailbreak your iPhone 5 and iPad mini. The evad3rs jailbreak team are well on their way towards releasing their untethered iOS 6 and iOS 6.1 jailbreak.
As of the time of this writing, the progress bar says it’s 99 percent done. They are under final preparations to get this thing out. Stick around, because it’s coming very soon. Keep an eye out.