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.
The orange rhombi have interior angles which measure 30 and 150 degrees. For the blue rhombi, 60 and 120 degrees are the measures of the interior angles.