In almost all the books on field theory I've seen, the authors list out the different types of quantities you can construct from the Dirac spinors and the gamma matrices, but I'm confused by how these work. For instance, if $$\overline\psi\gamma^5\psi$$ is a pseudoscalar, how can $$\overline\psi\gamma^\mu\psi$$ be a vector? Aren't gamma-5 and gamma-mu just different matrices? How do you get a vector out of the second operation? Thanks!