That is most likely to be a display card problem.
Be sure the card and the inside of the Mac Pro has the dust blown out (most vacuum cleaners generate large static charges, and should be avoided).
If problems continue, remove and re-seat the display card.
The 5770 is a nice replacement card if it comes to that, and works in all models of Mac Pro. Drivers are in 10.6.5 and later.
Thanks for the quick reply. I usually use compressed air to blow out interior dust. Is that a good idea? Also, not sure where the graphics card is. I am comfortable opening up the Mac Pro as I have installed additional hard drives, an airport card, etc. but admit not knowing where the graphics card is. Any easily identifiable "markings"?
As suggested removing and reseating the card may clear some possible corrosion buildup on the pins.
Also, if it is a video card problem, this may not help, but you might also try doing a smc reset too (unplug machine for at least 15 seconds and reboot after that).
Blew out the computer this afternoon. Lots of dust inside. (That's what happens in this econmy when you have to let the housekeeper go and dust builds up in the room. Oh well.) Anyway, all seems to be working fine, for now. It doesn't happen all the time so we'll see where we are in a day or so. Thanks so much for the input, really appreciate it. Love the Apple Support Communities!