Sure! For most of my desktop analysis of the amp section I used the Sennheiser HD800 and Sony MDR-7506 headphones. I tested it in portable environments with the Mee a151p, Oppo PM-3, and (forgive me for I have sinned) Apple earpods. I tested the line out directly into JBL lsr305s (paired with a SVS SB-1000), Eve sc207s, and Yamaha NS10s. I also tested the line out into a Schiit Asgard, Schiit Valhalla, and an Allen & Heath QU-16 Mixer.
With the Mee a151p and the Apple Earpods, I heard a noticeable noise floor from the E5s, which did not occur on my iPhone 4s headphone output. When paired with the HD800's, it drove them with plenty of power, but even in factory default settings with all SFX turned off, there was still a noticeable amount of distortion. Applying the inbuilt EQ drastically increased the distortion levels (I made sure it was not clipping). 3rd party EQ software did not have this problem.
My time with the Oppo PM-3 was brief, but in my honest opinion they sounded better out of my iPhone. I don't remember enough of those listening sessions to point out specifics. I don't think they had any real issue with noise.
It seems like distortion was a constant battle for the E5, especially since any little provocation in the settings would drastically increase THD measurements (I believe at one point I even read a full 10%). Even just changing volume settings in the internal mixer caused the distortion to spike, and it seemed that sometimes (even after manually resetting each individual slider and effect to what I thought would produce the best result) I could not reduce the THD to match the listed specifications without resetting the device.
Line out was a bit of a mixed bag. When connecting the line out to either of my active studio monitors or an external mixer/amplifier rack, the noise floor was VERY noticeable, and it was sometimes hard to get the signal to noise ratio low enough so I could enjoy a quiet movie, much less listen critically to a mix. When connected to the Schiit amplifiers and listening through the HD800, the noise floor was present, but quiet. However, the distortion was beyond unbearable until I thought to measure the output levels and discovered the line out of the E5 was quite a significant amount higher than the 1.2V rms standard. A reduction to 75% volume output solved this issue, and the E5 became rather pleasant as a DAC/preamp.
I don't mean to sound rude (I really don't, sorry if it comes across that way), but I'm honestly quite surprised that these complaints about the amp stage were new to you. I've seen many people on Head-Fi complain about the amp stage, and ZeosPantera (famous Reddit and Youtube reviewer) did a comparison with similarly priced DAC/Amps where he thought the amplifier on the E5 was so bad that he flat out refused to even acknowledge the E5 as a contender.
This is my second E5, as the first one experienced battery failure and had to be sent back for RMA. I remember the first one having similar problems with distortion, though I don't remember one way or the other with regards to noise floor. At home, my current E5 is leading a somewhat comfortable life as a microphone for my gaming sessions and as a Bluetooth headphone amplifier for when I'm out an about the house. When I'm out traveling I'll bring it with me as an airplane buddy, and when I'm out doing a show it'll stay in my back pocket as a "just in case" interface that I can set up with my phone.
I honestly LOVE the E5 for what it does, and it's an indispensable tool for daily use whose portability I wouldn't trade for anything.
HOWEVER, I honestly don't think it's an amazing performer for audiophiles. I really don't. This is a "jack of all trades ace of none" kind of device, and in the audiophile world people expect devices not just to meet sound quality standards but to blow them away. Marketing the E5 as a "Portable Audiophile DAC/Amp and putting it up against the like of the Teac HA-P50 and the XDuoo XD05 is kinda odd. It feels like a 200 input, 15 codec, wifi enabled, surround home theater console with a headphone jack trying to compete with a room full of hardcore, class A, 200 lb, monster dedicated headphones amps to see who can drive the HE-6's the best. It's the wrong competition.