It was called the Five Families War, because after Michael killed Sollozzo and Captain McCluskey, all the families turned against the Corleones, as Tom Hagen had predicted.

Remember this line:

Now nobody has ever gunned down a New York police captain -- never. It would be disastrous. All the Five Families would come after you, Sonny. The Corleone Family would be outcasts!


"It was between the brothers Kay -- I had nothing to do with it."