I spent most of the afternoon listening to my 5LE's on my Hifiman EF-5 amp. The main purpose was to finally roll all my 12AU7 tubes (~7 tubes), as well as a 12BH7.
The 5LE are special headphones: Capable of deep/impactful, but taut and natural bass with a nice balanced non-syrupy mid-range - and nice extended highs that never make you feel like you're missing out on anything. They're quite fast with the right amp, and they do respond and modify their sound with different tubes. I even tried different cables and opamps in the EF5 and thought I could detect some slight differences, though the tubes seemed to make the most difference.
If I want to listen to the music closest to the way I think it was intended/recorded, these are the right cans for that.
I've also owned the DT880/600's, which I found a bit too thin overall and mids a little recessed/thin in particular, even from the Bottlehead Crack which is supposed to be a good amp to pair it with.
I also had the HE500, which is a nice set of cans, but I didn't feel they were quite as balanced/uncolored as the 5LE's - a little accentuated in the midrange and a little rolled off/veiled in the highs - this is running off the EF5 as well as speaker taps (so power wasn't a problem). But if someone preferred the HE500, I could understand that.
I still own HD650's, which are, to me, a great complement for the 5LE. The 650 is similar enough to the HE500, but even a bit softer around the edges. Colored, but in a good way. Full, meaty, and great for when you don't want any fatigue even with less than stellar recordings.
With these two cans, I don't have the desire for any others.