It would be called a pentagonal pyramid. If you need an example just look at this website: http://en.wikipedia.org/wiki/Pentagonal_pyramid
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I would guess it is a pyramid that has a seven-sided polygon as its base.
If you mean the base has 4 sides then the pyramid is a square based pyramid and has 5 corners. If you mean the pyramid has 4 faces then the pyramid is a tetrahedron with a triangular base and has 4 corners.
It is a pyramid with a 57 sided polygon as base.
A pyramid can have any polygonal shape for its base. A pyramid with an n-sided polygonal base has n+1 vertices and n+1 faces.Assuming you're talking about a square pyramid, there are 5 faces and 5 vertices.
A prism with an n-sided base will have 2n vertices. A pyramid with an n-sided base will have n + 1 vertices. 6, 4, 8 and 5 vertices respectively.