This screen is caused by something called a " Kernel Panic".
This indicates there is something wrong with your Mac that is affecting OS X's base Unix core code seed or " Kernel"
Many things can cause this. Most of the time it is a piece of bad hardware.
It could be a RAM stick/s going bad, graphics card issue, logic board issues and/or hard drive issues or problems with your Mac's power supply.
It could, also, be caused from a failing PRAM battery.
What year and model is your G5? Has the PRAM battery ever been changed?
They only last between about 5-7 years before they need to be replaced.
If this is the original battery, it maybe time to replace it with a new, fresh one.
PRAM battery can be purchased cheaply here