The E5 does have a bass boost, but it seems like it's actually a bass reducer. That is, with bass boost on the bass level sounds a lot more like the source, and turning off bass boost seems just to throttle the original bass.
Might be worth it to invest in a decent player, maybe something which could be rockboxed so you can mess around with the EQ. I can't help but recommend the Clip+ (cheap, tiny, great SQ, rockboxable, etc.). Incidentally, I thought that there was much better quality coming straight out of the Clip+ than by using the E5.