Can G5 OSX 10.4 upgrade to OSX Mavericks

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You have got a PowerPC Mac, which can only run Mac OS X 10.5. OS X 10.6 and later are only compatible with Intel Macs.

If you want to use OS X Mavericks, get a new Mac, but if you want to upgrade your Mac to the most recent version, see if your computer is compatible with Mac OS X Leopard > http://support.apple.com/kb/sp517 You can buy Mac OS X Leopard at Amazon

Note upgrading to 10.5 or later will disable Classic applications on your G5. Those relate to pre-2001 applications that run when you use the Classic System Preference.