A triangular prism
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 3D shape with 10 vertices, 15 edges, and 5 faces is known as a pentakis icosidodecahedron. This polyhedron consists of 12 regular pentagonal faces and 20 triangular faces, resulting in a total of 5 faces when considering only the pentagonal ones. It can also be seen as a modification of an icosidodecahedron, where pyramids are added to each of the 12 pentagonal faces.
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.
pyramid
cube
A pyramid
cube
It is a square based pyramid that has 5 faces, 8 edges and 5 vertices
It is a triangular prism that has 6 vertices, 9 edges and 5 faces.
A triangular prism.
Triangular prism
It cannot be a simply connected 3d shape because it does not satisfy the Euler characteristic.
A shape with 5 faces and 5 vertices is a quadrilateral based pyramid
It is a triangular prism that has 6 vertices, 5 faces and 9 edges
A pyramid with a quadrilateral base. * * * * * A triangular dipyramid or a quadrilateral based pyramid.