Using the DVI->VGA adapter that came with the G5, and then adding an HD15->DB15 adapter (like the ones that came with the PowerBook G3 models and blue and white G3's), it should work just fine.
There would be no "slowdown" -- monitors just don't work like that. Only resolution and color depth make any difference. The old one will cause identical system performance to a modern monitor at the same resolution. (Mac OS X should always be run at 24-bit, so that's a non-issue as well.)
tooki