The War of the Five Kings was a large, multi-theater conflict fought in the Seven Kingdoms from 298AC until 300AC. As the name implies, over the course of the war five men claim the title of king: Joffrey Baratheon, Stannis Baratheon, and Renly Baratheon all claim the Iron Throne, whilst the separatists Robb Stark and Balon Greyjoy attempt to secede their lands from the rule of the Iron Throne, claiming the titles of King in the North and King of the Iron Islands respectively.
In 298 AC, the Hand of the King Jon Arryn dies of a sudden illness. King Robert Baratheon names his old friend and comrade Eddard Stark, Lord of Winterfell and Warde, of the North, as his Hand of the King. At this same time, two murder attempts are made on the life of Eddard's second son, Bran. Catelyn Stark, Lord Eddard's wife, would eventually suspect Tyrion Lannister and arrest him.
Tyrion Lannister is declared innocent through trial by combat, but not before Tywin Lannister, Lord of Casterly Rock and the Warden of the West, calls his bannermen. In King's Landing, Robert Baratheon is killed in a hunting accident. Soon after, Eddard is arrested for treason after trying to arrest the Queen Cersei Lannister and her children on the suspicion that they are progeny of incest. While the heir to Winterfell Robb Stark marches south with his bannermen to free his father, Eddard Stark is suddenly executed by King Joffrey Baratheon. In response, the North calls for the independence and Robb is chosen as their king.
Stannis and Renly Baratheon each declare themselves the rightful king of Westeros on the basis that Robert's children are bastards conceived by Cersei and Jaime Lannister. Renly is killed promptly, with his Stormlands bannermen flocking to Stannis and his Tyrell bannermen dispering.
As Robb Stark battles Tywin Lannister in the Riverlands, Balon Greyjoy declares the Iron Islands independent. He invades the North, burning down Winterfell and presumably killing Bran and Rickon Stark.
Stannis attacks King's Landing in the Battle of the Blackwater, but is defeated by the newly unified forces of Lannister and Tyrell. He would later go the Wall and defend it from Mancy Rayder's Wilding Army.
After losing a portion of his army after executing Rickard Karstark, Robb attempts to reconcile with Walder Frey. At the Red Wedding, Robb, his mother Catelyn, and most of the Northern lords are betrayed and killed by Frey and Bolton men.
In 300 AC, Joffrey Baratheon is assassinated during his wedding to Margaery Tyrell. The ensuing events would include the deaths of Oberyn Martell and Tywin Lannister and flight of Tyrion from Westeros.
In the North, Stannis is killed during a battle with Roose Bolton's forces while trying to gain support.
In the Iron Islands, Balon Greyjoy dies and his brother Euron Greyjoy is chosen as king. He too would go on to continue the aggression towards the Seven Kingdoms.