The 5th century BC started the first day of 500 BC and ended the last day of 401 BC.
This century saw the establishment of Pataliputra as a capital of the Magadha Empire. This city would later become the ruling capital of different Indian kingdoms for about a thousand years. This period saw the rise of two great philosophical schools of the east, Jainism and Buddhism.
This period saw Mahavira and Buddha spreading their respective teachings in the northern plains of India. This essentially changed the socio-cultural and political dynamics of the region of South Asia. Buddhism would later go on to become one of the major world religions.
This period also saw the work of Yaska, who created Nirukta, that would lay the foundation stone for Sanskrit grammar and is one of the oldest works on grammar known to mankind.
This century is also traditionally recognized as the classical period of the Greeks, which would continue all the way through the 4th century until the time of Alexander the Great. The life of Socrates represented a major milestone in Greek philosophy though his teachings only survive through the work of his students, most notably Plato and Xenophon. The tragedians Aeschylus, Sophocles, and Euripides, as well as the comedian Aristophanes all date from this era and many of their works are still considered classics of the western theatrical canon.
The Persian Wars, fought between a coalition of Greek cities and the vast AchaemenidPersian Empire was a pivotal moment in Greek politics. The Greeks successfully prevented the annexation of Greece by the Persians in Battle of Plataea, Battle of Mycale, and further counter attacks. Afterwards, Sparta, the dominant power in the coalition, had no intention of further offensive action and considered the war over. Meanwhile, Athens counter-attacked, liberating Greek subjects of the Persian Empire up and down the Ionian coast and mobilizing a new coalition, the Delian League. Tensions between Athens, and its growing imperialistic ambitions as leader of the Delian League, and the traditionally dominant Sparta led to a protracted stalemate in the Peloponnesian War.
426 BC: When Ambracia invades Acarnania, they seek help from the Spartans and Athenians respectively. The Athenians then defeat the Spartans in the Battle of Olpae.
424 BC: Sicily withdraws from the war and expels every foreign power. Thus, Athens is forced to withdraw from the island.
424 BC: The Athenians try to capture Megara, but are defeated by the Spartans.
424 BC: The Spartan general Brasidas captures Amphipolis, which is a setback for Athens. Thucydides is held responsible for the Athenian failure and is ostracised. This gives him time to start writing his history book.
423 BC: The Athenians propose a cease-fire, which the Spartan general Brasidas ignores.
416 BC: The Athenians capture the island of Melos and treat the inhabitants with great cruelty.
416 BC: The Athenians adhere to a plea of help from Sicily and start planning an invasion of the island.
415 BC: The sacred Hermae busts in Athens are mutilated just before the expedition to Sicily is sent away. One of the culprits, Andocides, is captured and is forced to turn informer. He names the other mutilators, among them Alcibiades, who are sentenced to death in their absence.
415 BC: Alcibiades defects from Athens to Sparta after having learned about his death sentence.
414 BC: The Athenians try to make a breakthrough in their siege of Syracuse but are defeated by the Spartans.
413 BC: Demosthenes suggests the Athenians leave Syracuse in order to return to Athens, where help is needed. However, Nicias refuses and they are again defeated in battle by the Spartans. Both Demosthenes and Nicias are killed.
411 BC: The democracy in Athens is overthrown and replaced by the oligarchic Council of Four Hundred. This council is itself soon defeated and order is almost restored, when the Five Thousand start ruling. Early next year, they are also overthrown and the old democracy is restored.
408 BC: The Persian king, Darius II, decides to aid Sparta in the war and makes his son Cyrus a satrap. However, Cyrus starts collecting an army to benefit his own interests, rather than his father's.
408 BC: Alcibiades returns to Athens in triumph after an absence of seven years.
407 BC: The Athenian fleet is routed by the Spartan one in the Battle of Notium, which gives Alcibiades' opponents a reason to strip him of command. He never returns to Athens again.
403 BC: Some exiled Athenians return to fight the Thirty Tyrants and restore democracy in Athens. They are, however, narrowly defeated by the Spartans in the Battle of Piraeus. After this, the Spartan king Pausanias allows democracy to be restored in Athens.
403 BC: Thrasybulus restores the Athenian democracy and grants an almost general amnesty.
400 BC: After Cyrus has been killed, his Greek mercenaries make their way back to Greece, where Sparta is so impressed with their feats in and march through Persia that they declare war on the Persians.
The Chinese philosopher Li Kui writes the Book of Law (Fajing, 法经) in 407 BC, the basis for the law codes of the following Qin dynasty and partially that of the Han dynasty.
Scholars commonly accept that the Hindu text the Bhagavad Gita was written.
^Zhao, Dingxin (2004). "Comment: Spurious Causation in a Historical Process: War and Bureaucratization in Early China". American Sociological Review. 69 (4): 603–607. doi:10.1177/000312240406900407.