The five families and their bosses are (currently):
Bonanno: Michael Mancuso
Gambino: Domenico Cefalu
Genovese: Daniel "Danny the Lion" Leo
Lucchese: Steven Crea
The Colombo family was once known as the Profaci Crime Family, until a coup caused a name change in the early years of the Bonanno Family to the Massino Family but since his arrest and defection it is unlikely to happen. The DeCavalcante crime family, based in nearby Elizabeth, NJ, also has ties to the five New York families.