Why do we call 5th century BC Greek the Classical period?

Classics

The word Classics is derived from the Latin adjective classicus, meaning “belonging to the highest class of citizens”. The word was originally used to describe the members of the highest class in ancient Rome. By the 2nd century AD the word was used in literary criticism to describe writers of the highest quality. For example, Aulus Gellius, in his Attic Nights, contrasts “classicus” and “proletarius” writers.

The writers of 5th century Athens were considered to be the pinnacle of Greek writing—the orators, the dramatists, the historians. (Not so the poets, which was more an 8th to 6th century thing.) Their version of Greek was considered the most prestigious and was the model for all subsequent writing.

So they were the classical authors—the authors of the highest class, as judged by subsequent Latin-speaking generations; and their period was called the Classical period.