Mate in 5

Doing a little research I've decided that there are essentially 4 ways to checkmate your opponent is 5 moves or less, from the start of the game.
The basic patterns are 

• Fools Mate (1.g4 e6 2.f4 Qh4#)
• Touch Move (1.e4 e5 2.Qh5 Ke7 3.Qxe5#)
• Scholars Mate (1.e4 e5 2.Qh5 Nc6 3.Bc4 Nf6 4.Qxf7#)
• Nd6/Nd3 (1.d4 e5 2.dxe Nc6 3.Nf3 Qe7 4.c3 Nxe5 5.Nbd2 Nd3#)

Of course there are variants on these themes and even a combination of ideas (eg 1.e4 e5 2.f4 Bc5 3.fxe Qh4+ 4.Ke2 Qxe4#), but the general approach is limited.
As for the names Fools and Scholars Mate are well known, although most people refer to Scholars as "The four move checkmate". The "Touch Move" label comes from the story that under old rules of chess, if you touched a piece that could not move, then you had to move your king instead. In the example game, Black went to play Nc6 on move 2, but picked up the Bishop on c8 instead, and was forced to move his king to e7. I couldn't find a name for the last mate, but was tempted to christen it "Alekhine's Mate" after a famous version of it in a simul he once gave.