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.