A quadrilateral based pyramid, of which a square based pyramid would be a special case.
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A five sided 3d shape is called a pentehedron
It is a pentahedron. One example of an irregular pentahedron is the 4-sided pyramid.
A pyramid which has a total of 5 faces is a quadrilateral based pyramid.
A 3d shape with 5 faces can be a square pyramid
It would be called a pentagonal pyramid. If you need an example just look at this website: http://en.wikipedia.org/wiki/Pentagonal_pyramid