Well the newer TimeMachine model as stated in current Support pages isn't directly compatible on OS X 10.5 now, as noted in above link provided.
What OS X does your newer MacBook have running in it? (Not linux?)
With the current setup you have there may be a way -among other details in the support page- to do the migration of data from Mac, including a subnote on Time Machine, in a section below the main article with triangle by it, from links here:
•OS X: How to migrate data from another Mac using Mavericks 10.9:
http://support.apple.com/kb/HT5872
•OS X: How to migrate data from another Mac using Mountain Lion 10.8 and Earlier:
http://support.apple.com/kb/ht4889
In the support articles there are various troubleshooting and help items about the technology, some data back some time and whatever still stands would be there. Some archives are no longer current and say so.
Perhaps someoone still using older PPC Macs and Leopard 10.5, will say how to backup into a G4 PowerBook, from a Time Machine.
Unless the TimeMachine backup from the older PPC G4 PowerBook is used in the migration process of transferring personal account files from there to a new MacBook running (?) OS X. This probably could be done. You may be able to access older libraries, such as iPhoto, iTunes, etc and import them from the archive, to a newer Intel-based MacBook.
Sorry for any confusion.
I'll more carefully reply in the future.
Good luck & happy computing! 🙂
PS: a different direction on archives, time machine, clones, and other devices:
•About Time Machine - Time Machine vs. Clones and Archives:
http://pondini.org/TM/Clones.html
•Apple OS X and Time Machine Tips:
http://pondini.org/TM/Home.html
{edited to add link details}