In my experience it's hard to beat a properly setup HD560s, of which I'm most taken by a properly setup (EQ'd) New Version HD560s (more so than the Old Version). I've recently been trying an EQ'd HD800 and currently the optimised HD560s is sounding better, but I haven't spent much time optimising the HD800 yet (and I'll wait until I've been through some earwax removal (lol) which is happening in a few weeks). So I think most people can be happy that an EQ'd HD560s is pretty close to the best possible headphone experience as it's very capable in all areas of the frequency range without any real weaknesses - I think it gets to a point where there's not really much to be gained by "chasing headphones". Re Discord, I've never used it, but I'll continue to give you replies on here.
It sounds like there might be a problem with your particular unit of HD560s. I did have to send one of the New Version units back to Amazon because it had noticeable channel imbalance, so maybe there's a few duff units out there that aren't performing properly. What you could do is send it back for another HD560s, particularly if you got it off Amazon. You shouldn't have to crank Bass & Treble dials to max, eventhough I don't know how extreme Fosi K5 can go with those dials. Really the HD560s normally only needs subtle EQ to be perfect, so could be something wrong with your unit. Getting a replacement unit would rule that out, and then if you still don't like it then you're probably just after (or used to) a very different type of sound that steers away from "the average".
EDIT: quickly googled Fosi K5, it seems very unpredictable re the frequency response:
Fosi Audio K5 Pro Gaming DAC/AMP Review There is a severe lack of good DAC/AMPs with a decent microphone input on the market, there are a lot of cheap dongles and no-name soundcards, but nothing that stands out. If your using a Gaming Headset which probably costs like 100-200€ you will have...
www.audiosciencereview.com
Haven't looked into this further, but it seems that you'd be better off getting a more neutral DAC/amp, as could well be the Fosi K5 screwing up the neutrality/balance of your HD560s. I'd try your HD560s with some other audio chains first, even just plugged into your phone or PC or whatever if you don't have any other dedicated DAC/amps.
Fosi K5 is being completely trashed in that thread, definitely try your HD560s with some other gear before you return it for a replacement! I don't think you can hope to successfully evaluate & EQ the HD560s using that Fosi K5, that's probably what the problem is.