The argument of Republic 5 is one of the most difficult in the Platonic corpus. It is crucial for an understanding of both Plato's epistemology in general and also the specific political proposals of the Republic. I will start by offering some contextual information, and then lay out the argument as a whole. I will then offer a general explanation of the concepts of knowledge, belief, and existence, operative in the argument. Finally, I work through the main steps more slowly and with explanation as appropriate.