There are dozens of possibilities for a 5 move checkmate. You could use the 4 move checkmate "Scholar's Mate" and just delay a move in it, you could use a reversed Scholar's Mate and just use it as black. Or, you could find a different combination such as this sequence: 1. d2d4, e7e5 2. qd3, nc6 3. qb3, d7d6 4. bg5, qxg5 and 5. nf3 qc1#. Or any number of similar sequences.
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Follow this step by step. (Note that this is checkmating the white king.)
1. First, move the pawn above the bishop on the right north by 2 squares. (F2-F4)
2. Next, black moves their pawn below their king south by one square. (E7-E6)
3. Then, move the pawn above the knight on the right north by 2 squares. (G2-G4)
4. Finally, black will move their queen south-east by 4 squares. (D8-H4)
That is how you can do a two move checkmate in Chess!
Your opponent is check mated when he cannot move anywhere away from the check position that you've just put him in.