A triangular prism
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A pyramid
There is no such shape. The only convex shape that has four faces is a tetrahedron, and that has four vertices, not 5.
A triangular prism fits the given description
A pyramid has the same number of faces as vertices. A triangular pyramid has 4. A rectangular pyramid has 5. Check into Euler's Theorems.
The numbers in the question do not satisfy the Euler characteristic so there cannot be such a [convex] polyhedron.