It seems as though the first private server to fully support the 5.0.5 patch of Mists of Pandaria is Pandashan. After 4 months of the release of Mists of Pandaria, it seems as though the private server Pandashan has released it’s server on the 2nd of Janurary 2013. The private server already has a booming 31k likes (compared to the lifetime 128k likes of Molten) and they have recently made a facebook event that have noted that the server has had over 4000 players online at a time.
I haven’t really researched much into the private server, but it does seem very promising, considering it’s the first private server, and the amount of players the server has been holding (although I do admit after skimming through the facebook page and forum posts about the game, players have been having lag). Currently as I’m typing up this article, I can see 1k players logged in to the US realm and 600 players logged into the French realm.