Carry it on the plane with you.. or your friend.
If it's "health related", and urgent... I'd seriously consider looking at other countries around you to get what you need, and go to get them. HK or Thailand if you're lucky.. or go east to Taiwan or Japan - even South Korea.
I can't think of any other options that can get something from any country overseas in past Chinese customs in less than the 5 days you're talking about!
Ups says they have three day air but they would probably get delayed five days
So your best bet would probably be to bribe someone witch I do not condone