You have two pieces one has 5 faces the other 7.
You and your friend are talking about different pieces.
![Two parts of a cube][2]
The piece on the left has a total of 7 faces (5 that were on the outside of the cube and 2 that are formed inside by cutting.)
The piece on the right has 5 faces (3 that were on the outside of the cube and 2 that are formed inside by cutting.) [2]:
The shape enclosed by the points is the one on the right https://i.sstatic.net/rp1qd.png(5 faces) the piece left over is on the left (7 faces.)
