Sorry to hear about your issue! I just played the sample you provided at a pretty-high volume and could not perceive any rattling in my T5p's.
The T5p does not utilize any screws or locking mechanisms in the assembly of the drivers/cups so my 1st step in troubleshooting this would be to make sure that the driver is pushed firmly into the headphone assembly and that the rubber seal is in place.
Here is a picture (taken from Zynsonix's re-cable-tutorial) of the driver (on the right of the picture) + rubber seal (the ring on the left of the picture) for reference:
Couple questions for you:
1. Does the issue occur in both channels?
2. Are you EQ'ing the bass up at all? (I have found that raising the bass any more than +2db can cause distortion)
Hopefully that helps