Neutral (flat, not Harman) open back with better bass extension, treble extension and soundstage than the 600 series, and the best clarity yet from the 500 series (but not 600 series level). There's some minor treble spikes (to promote soundstage) that some can perceive as higher still due to how the drivers are angled.
These would be great open backs for gaming, pretty much any music genre (including EDM-based tracks, which normally lose a bit with open backs), but doesn't have quite as natural a presentation or timbre as the 600 series (particularly the HD 600 and the 650/6XX), and the 6XX would be about the same price via Drop.
For those that are looking for something a little spicier still from Sennheiser, Drop has announced the Sennheiser HD8XX tonight, so if you've got $1500 sitting around, that might be and end-game option if you can bide your time while they produce the product.
Reviews:
https://www.rtings.com/headphones/reviews/sennheiser/hd-560s
https://diyaudioheaven.wordpress.com/headphones/measurements…
https://www.headfonia.com/sennheiser-hd-560s-review/
Description is spot-on , on par with my own listening and others'