Is the card running hot requiring it to run at a higher speed? I have a 2010 mac pro too (got it November 2010) but generally don't hear a "high pitch" sound from it. Occasionally the fan may rev up but the sound isn't high pitched.
Consider adding a temperature monitor. I use iStat Menus which can read the pci slot 1 temp (can't read video card temp directly). Others that may work are iStat Pro, Temperature Monitor, Hardware Monitor, and probably others.
FWIW, I am on my third 5870 (thank goodness for AppleCare)! First two suffered the problem of the fan motor either not overcoming the starting friction to get the fan going or would just stop rotating the fan. End result is a thermal cutoff (card overheats) and the machine shuts down (except for one exhaust fan). This is one of the main reasons I installed iStat Menus in the first place.
So based on my experience with 5870 fans I would say a high pitched sound may be that the fan bearing is failing. Just a theory of course. But when it comes to 5870 fans I am beginning to think anything is possible. 😢
