Hmmm... I really don't get this, sorry, with an input volume control on the back of the speakers, and line, TRS (balanced and unbalanced) and XLR balanced inputs you should be able to interface with ANY media devices out there...There should be NO reason for any interface devices with this level of control. Now, there may be a problem with either the line outputs of the DAC, or the line inputs of the E5 (even the cable could be bad...), but if you turn the volume control down and still have distortion, there is something other going on here...Line level is line level, and is plug and play throughout the audio multiverse...
Have you tried the other inputs to the speakers to verify if there is a problem with them? Have you tried a different line level source into the speakers? are BOTH speakers sounding bad?