What is a shape with 5 faces?

A shape with 5 sides is a pentagon.

However, the term face is only applied to three-dimensional forms,

and a shape (solid) with 5 faces is a pentahedron.

There are no regular pentahedrons. The two forms are the square pyramid and the triangular prism. The former has 4 triangular sides and a square or rectangular base; the latter has 3 rectangular (or square) faces and two triangular ends.