It is not possible to tessellate a plane using only regular pentagons and decagons, but that doesn’t stop me from trying. To get this to work, I had to add rhombi and concave pentagons — but even then, it’s an aperiodic tessellation.
An Aperiodic Tessellation Featuring Regular Decagons and Regular Pentagons, Along With Concave Pentagons and a Few Rhombi
RobertLovesPi.net 
Following in the footsteps of Kepler who also tried many ways. I like this one: https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Kepler_decagon_pentagon_pentagram_tiling.png/497px-Kepler_decagon_pentagon_pentagram_tiling.png
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