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There are infinitely many possible answers. A square based pyramid is one.
A square base, and four triangular shaped sides equals five flat surfaces.
It has 5 flat faces because there are 4 flat faces at the top and 1 flat face at the bottom.
a pyramid with a triangular base has 4 faces. a pyramid with a square base has 5 faces.
This is a popular topic, discussed in many places on the web. The attached link is one place that I like. If you want to look for others just google for surface area square pyramid.