Final Cut Pro 4 and 4.5 requires an AGP Graphics card to run and consequently will not run on the newly announced PCI Express based dual core and Quad PowerMacs, which use a PCI Express Graphics Card. Final Cut Pro 3 will not run on OS X 10.4 Tiger so it will also not run on the new PowerMacs, which require 10.4 as a minimum.
To use Final Cut Pro on Power Mac G5 (Late 2005) you should upgrade to Final Cut Pro 5.
Final Cut Express HD will run on the PCIe PowerMacs by updating to version 3.0.1 released today. See previous news item on updates to Final Cut Pro 5 and FInal Cut Express HD.