A decahedron.
Some decahedron shapes are a nonagon-based pyramid, an octagon based prism, or a pentagon based di-pyramid.
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octagonal prism and decahedron
A cube has 6 faces. The number of faces, alone, is not sufficient to figure out the number of edges. For example, a cube has 12 edges. A pentagonal pyramid also has 6 faces, but it has 10 edges.
There can be no such shape.
It is a pentagonal prism
If it also has a pentagonal face then a pentagonal pyramid. Else it does not exist.