Nice to see that one finally tested here.
A5X/A7X have always been an either love or hate thing for people, somehow.
I'm in the hate group ;-) I cannot stand listening to A7X for more than an hour or so... A5X is slightly better but still a lot of fatigue going on. It really depends on music style. Hit them with EDM or Techno or simple "girl & guitar" and the typical test tracks with sparse instrumentation and I find then sounding literally brilliant and crisp and "exiting" (at least at first impression).
Hit them with dense orchestral or just a simple grand piano, they quickly fall apart for me, at almost any listening level. Has nothing to do with the port notch or the Klaus Heinz "House EQ" (tilt up at both frequency extremes).
I attribute this partly to the woofer power amp. In the early models we used one half **) of TDA8920 (PWM chip amp) for this but when it became obsolete we changed to TDA8950 or 8953 and that one is a truly broken design. Decaying piano notes sound like Digeridoo on those if you listen closely. On the ARTist5 which is technically identical (except for some add-ons) but uses TDA7294's for woofer and tweeter this "layer of confusion" during softer passages of the music is not present. It also has a rear-firing slot port with zero issues (apart from a bit of chuffing).
**) original plan was to use the other half for the tweeter but buzzing crosstalk from woofer channel and the general disortion characteristic was unbearable so we changed the A5X electronics in a last-minute overhaul to use the class-A/B amp on the tweeter. The TDA8920 thus was broken too, for a use case like this. Specs say cross-talk is -60dB (0.1%) @1kHz which would be considered OK but the don't tell us the spectrum of the crosstalk which is basically a high pass filtered full-wave rectified copy of the woofer channel current. Every time the woofer current reverses direction at a zero crossing there was a glitch in the tweeter (which is high sensitivity, pronouncing the issue).
The second factor is cone breakup, IMHO. This cone (more exactly, the dustcap) has strong unsupressed resonances. A third factor is the tweeter distortion near it's XO point.
As ususal, these distortion issues are not showing up so clearly in simple swept/stepped sine measurement. You have to use 2-tone or full IMD to see that and get closer to what is actually heard.
The port issue is just bad luck where a number of factors conincided. The "pan-flute" resonance exited by the front wave happens to be in phase with the exitation from the back wave so their energies combine rather than (at leasty partly) cancel each other. This looks very bad on plots but is IHMO much more benign than the other issues. Yet another one of those is severe port chuffing.
So this is a speaker that has issues at low levels and has other issues at high levels. Both contribute to often mentioned "detail" and "crispness" of these speakers but in the end this is false detail and false crispness.
But, since a monitor is just a tool, when you are aware of its characteristics this actually is not a drawback. It forces you to EQ, mix and produce your stuff in a certain way so that it doesn't trigger too much of the ill-effects and then it will sound good on "typical" (lesser) consumer speakers or PA's as well, many of which will have similar issues. This is IMHO one reason why A5X/A7X was such a successful product, notably within the EDM home-producers scene which skyrocketed at the time..
Note: You've sure noted the wording "we" in this text... I was just starting my day job at ADAM at the time when AX series was launched, so I had no deal in their design. Rather my first task was to get the production up and running and fix the main issues, notably on that said A5X...
and they're good for losing weight, says my wallet 
