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Extra dimensions provide a natural way to define and regulate chiral gauge theories. In scenarios where we live on the four-dimensional boundary of a five dimensional world, anomalies are related to current flow into the extra dimension. A consequence is that our concept of universality might need to be altered. In particular, QCD as a stand-alone theory need not be in the same universality class as QCD embedded in the Standard Model. I discuss how lattice chiral gauge theories can be regulated in five dimensions, and show that a possible consequence is that the strong CP problem can be resolved without an axion — due to the appearance of fermion zero modes localized far from our world in the fifth dimension.