Your tiling is 1-isohedral, according to wikipedia.

Reinhardt (1918) found the first five pentagonal tilings. These all share the property to be isohedral, or "tile transitive", meaning that the symmetries of the tiling can take any tile to any other tile (more formally, the automorphism group acts transitively on the tiles). By contrast, all subsequently found tilings are k-isohedral, with k>1.

Thus, your tiling, if not new, is one of these five. My guess is that it is p4, (wikipedia notation), and it looks very similar.

Your tiling is 1-isohedral, according to wikipedia.

EDIT: Yoav points out that it is actually not 1-isohedral...

Reinhardt (1918) found the first five pentagonal tilings. These all share the property to be isohedral, or "tile transitive", meaning that the symmetries of the tiling can take any tile to any other tile (more formally, the automorphism group acts transitively on the tiles). By contrast, all subsequently found tilings are k-isohedral, with k>1.

Thus, your tiling, if not new, is one of these five. My guess is that it is p4, (wikipedia notation), and it looks very similar.