I think that for anyone "in the hobby", there is no excuse to not own a Stax headphone. Once I heard Stax, I didn't really bother with anything else. The older Stax headphones (and driver units) can be found for around 500$, and a brand new set of the entry level 252s driver united and SR-L300 can be had for around 800$ combined. To my ears, this sound is better than even the HD800. I think its the best "bang for buck" sound in the "pretty expensive" price range.
Edit: The OP asked for 5, so here they are!
Stax SR-L500mk2
Audeze LCD 2
Sennheiser HD800
Denon AH-D5000 / Massdrop TH-00
Stax SR-007
Reasoning:
Stax SR-L500mk2 is my current headphone and the one I prefer the most of all headphones I've heard to date
Audeze LCD 2 because it is very clean sounding, with a lot of bass and little listening fatigue. Minus points for comfort
HD800 because it has such a large and impressive headstage
Denon AH-D5000 / Massdrop TH-00 because it has a very fun sound signature that lends itself to many contemporary genres, while still being great for classical and more "treble focused" music. Fantastic allrounders
Stax SR-007 because it is one of the best headphones I've ever owned, with almost no flaws except maybe that I think the treble could be a bit brighter.