I'm using a MacPro 1.1, 3 GHz Dual-Core Intel Xeon processors, 5 GB Memory, currently running OS X 10.4.11. I have to upgrade to OS X 10.5 or 10.6 to upgrade some software. Any advice or warnings about which to go with on this mac?
Well whatever you decide, if you go 10.6 bookmark the site Mac OS X 10.6 Snow Leopard compatibility table. If you are using SMB with Windows hold off 10.6 until 10.6.5 (it has SMB fixes) plus it has some graphic fixes for some Mac Book Pros.
Plus if you have a blank disk in that Mac Pro you can follow the steps in the article How to Perform a Clean Install of Snow Leopard OS X 10.6 on that drive (IMHO Fresh installs are way better then 'upgrade' installs). Then in that drive use /Applications/Utilities/Migration Assistant to move pictures/email to that new 10.6 drive. IMHO this would be the best way to go to 10.6.