How to use iPhone 5 with a PowerPC?

Specifically an iBook G4 running Leopard. Is there an alternative to iTunes that will run on Leopard and connect to iPhone 5? (I'm totally cool with solution that requires a jailbroken device.)

No - I don't think it's possible.

You need a new version of iTunes to sync an iPhone 5 (any version released in the past few months) and I don't think they made a version for PowerPC.