https://diyaudioheaven.wordpress.com/headphones/measurements/brands-s-se/hd599/
There's a graph comparing the two directly. From what I can read from the graph and my experience with the HD5 series (I've only demoed, never owned), the HD5 series will be warmer but a bit grainier and less mid focused. I like bass, but I don't like them too warm without proper extension. HD58X fits almost everything I want out of a headphone.
Personally I think the HD5 series has a bit wider soundstage, but not by much. The HD58X's soundstage width is average where I felt the HD6XX felt absolutely claustrophobic. However the imaging for the HD58X is top notch and gives a real sense of depth compared to my other headphones. It's more of an enveloping sound rather than a wide "left to right" stage if that makes sense.