It might, cooler clearance is 165mm same as the D15 height. But you should get the NH-D15S for three reasons:
Cheaper and only 1-2C warmer and slightly quieter
Better compatibility with PCie slots/RAM due to its asymmetrical design and will avoid having to raise the front fan above the RAM higher than 165mm as can happen with D15, because there is no front fan, only the centre fan.
The D15S is actually 160mm in height, not 165mm as the OcUK description states. So will work for sure in the H500.
H500 can be a warm case and you'd get better temps in something like Meshify C (10-15C) with an air cooler. Then again, you may have case or the cooler already?