Just did a little back to back listen with the P5 and HD25 playing "Better Things" by Sharon Jones and the Dap Kings AAC 256kbps straight off iPhone source, eq turned off.
The first 30 seconds really separate the cans. With the P5 the sound is really nice and warm, but with the HD-25 I got a lot more separation of all the elements. The opening seconds feature some bass, bongo, horns, handclaps, electric guitar, piano, and some background noise of laid-back party conversations. The HD-25 brings everything out in the mid-range, and the background conversation is really presented well. When I pop on the P5 the same intro has a much different feel. The keys on the far left end of the piano suddenly appear out of nowhere (hardly noticed them in the HD-25 presentation) while all that cool background convo that sets the stage for the song is almost entirely obscured by the bass. Either way the presentation is very pleasing - it's just hard to say which is better.
That said, fiddling with the EQ at home I can approximate the P5 sound on the HD-25. I don't know if the reverse is true with the P5. On a completely different comparison, I have to say the P5s are super comfy and the earpieces rotate flat for storage quite nicely - unfortunately the cable looks a little too weak for my taste.
I also want to warn everyone that I'm a bit of a newbie to the headphone scene - just in case that colours how you view my assessment.