I would like to offer a counter argument to the existing answers. As mentioned the Maesters like to quibble that it was not "The War of Five Kings* because Renly was already dead when Balon made his claim.
HOWEVER, let us take an out-of-universe clue...
In the appendix for A Clash of Kings the first section in titled "The Kings and Their Courts" and are listed as follows:
- The King of the Iron Throne
- The King in the Narrow Sea
- The King in Highgarden
- The King in the North
- The Queen Across the Water
This would translate to:
- Joffrey Baratheon
- Stannis Baratheon
- Renly Baratheon
- Robb Stark
- Daenrys Targaryen
So my answer is that those are the original participants of the War of Five Kings. Later you can swap Balon for Renly and still have five active participants until the Red Wedding...
Feel free to quibble that one is a queen, you sexist pigs! GRRM felt it was worthy of calling out Daenrys specifically in the appendix...