There is an exploit for devices up to 5.6.7, but someone would need to do the steps to go from exploit to actual jailbreak.
There, erm, "may" be exploits in the current firmware, but I doubt anyone will discuss those until after 5.6.10 or later comes out.
In general, if you want to be jailbroken, just keep your device away from the Amazon mothership and be patient.
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