Chances are it's the sending unit has gone bad. Mine was exhibiting the same behavior before I changed it. Here's how to test it: Turn the ignition on, remove the wire from the sending unit and ground it. The gauge should drop from 5 to 0. If so, replace the unit. Here's a good thread that I followed when I did mine.
CAUTION: Don't try to just unbolt the sending unit from the engine. You MUST remove the oil line and hollow bolt first.
http://forums.pelicanparts.com/porsche-911-technical-forum/502982-another-oil-pressure-sender-replacement-thread-pics.html