Installing OSX onto PPC using Intel Mac and Firewire
There has to be a typo in the OPs question that can only be corrected by the OP:
The error message "10.3 cannot be installed on this machine" is out of place there.

To install OS X (maxing out at OS X Leopard 10.5.8) you have several options regarding the DVD: 


clean the DVD drive in the G5, the lens might just be dirty
clean the Installation DVD, the DVD might just be dirty, slightly scratched
get another Leopard Installation DVD that doesn't have these flaws


Using the Firewire and Target Disk Mode route should be possible too. 

But then there is the problem with "PPC to Intel transition": PPC machines boot from drives with an Apple Partition Map and Intel machines from an GUID partition map drive. 

That prevents booting the G5 form a MacBook in Target Disk Mode or if you just swap the drives out; although the contents of 10.5 installations would be the same on both machines. Using a GUID formatted drive in a PPC machine is the most likely reason for the "No-Entry"-sign: there is just no disk available the PPC machine deems bootable.

You can therefore 


boot into Leopard on the MacBook, 
mount the G5 in Target Disk Mode, 
format the G5 drive with an Apple Partition Map
then install Leopard onto the G5 from the Macbook (this can be forced using Pacifist)


This describes the clean way.  

Alternatively you could just clone the Leopard installation from the MacBook to the G5's drive.