In Plato's Protagoras (317c) he says that he is old enough to be the father of anyone present, including Hippias and Prodicus. This confirms that he was one of the earliest sophists and suggests the 490s BCE as his birth year.

When was Protagoras published?

Sprague (ed.), The Older Sophists (1972). A. Capizzi, Protagora (1955).

When did Plato write his dialogues?

Generally, the works which are most often assigned to Plato's early years are all considered to be Socratic dialogues (written from 399 to 387).