Final answer:
The height of Hellenic culture was during the Classical Age of Greece, characterized by artistic and intellectual achievements.
Step-by-step explanation:
The height of Hellenic culture was during the Classical Age of Greece, which lasted from the triumph of the Greek coalition against Persia in 479 BCE to the conquest of Greece by the Macedonian king Philip II in 338 BCE.
This era is best remembered for its artistic and intellectual achievements, particularly in philosophy with the notable contributions of Socrates, Plato, and Aristotle.
The Classical Age of Greece marks the period when Greek civilization reached its most powerful and innovative state.