In the 5th century BC, the main focus in Greek philosophy shifted from explaining natural phenomnon to examining human nature and generally anthropological issues.
In the beginning, this period is characterised by the conflict between Socrates and his students with the Sophists. Later, at the height of Classical Greece, Plato founded his academy. And finally, Aristotle (a student of Plato and teacher of Alexander the Great) lays down the foundation for all subsequent western philosophy until the Enlightenment.
Unlike with the Presocratics, we no longer have to rely on fragments and references, many books have survived in whole.