This is the corner-turning Starminx, dino dodecahedron or dinominx, depending on your preference. It is a dodecahedral version of a dino cube. To mix and solve the puzzle, you turn a triangle of 6 pieces (3 edges, 3 centres).
The starminx is a large puzzle and the pieces can catch a little at the points. Like the rainbow cube, it looks much harder to solve than it is. A turn moves so few of the pieces that solving becomes a matter of reduction, working your way across the puzzle. The things you would do with other vertex-turning puzzles work with the starminx too and make it fairly straightforward to solve intuitively.