Extended Cube 3x3x5
Extended cubes are made by gluing extra cubies onto layers of the cube. In this case, the outer layers of the puzzle are stuck to their neighbour. This means that the puzzle changes shape (the top and bottom layers have double-size cubies) when you scramble it.
You solve the extended cube just like you do the standard 3x3x3. The one in the picture is not of the highest quality but an interesting diversion from the norm.