Q: transfering data from 10.5.8 on a PPC IMac to Mavericks

OS X: How to migrate data from another Mac using Mavericks

Migrating from PPC Macs to Intel Macs:

https://discussions.apple.com/docs/DOC-2295

http://support.apple.com/kb/HT4796

and this article:

http://www.macworld.co.uk/mac/news/?newsid=3444778&olo=email

After a certain point update to Mountain Lion (OS X 10.8.x) , Migration Assistant all severed ties with the OS X version (Tiger) prior to yours, though it continued to work with Leopard. This may now be the case with Mavericks and Leopard, unfortunately I no longer have any Leopard systems to test so you will have to try it yourself:

Start the older Mac in Target Disk Mode. When asked "How do you want to transfer your information" select "From a Mac, PC, Time Machine backup or other disk" then click Continue. On the next screen be sure to select "From a Time Machine backup or other disk" and not "From a Mac or PC".

Determine if your new iMac is able to communicate with the older one in that mode. If it will not work, then manually copying files will be the only solution.

Mac OS X 10.4.4 is the oldest system you can technically migrate Intel to Intel.

PowerPC to Intel or Intel PowerPC are best done with Target Disk Mode and user tip 2295 mentioned above.

Mac OS X 10.5.8 is the newest operating system for PowerPCs.

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New iMacs have a Thunderbolt port. You can purchase a Thunderbolt to FireWire adapter from Apple. That adapter is FW800 only, and your older iMac is probably FW400 so you will need an appropriate cable. Apple sells them as well but there are other sources such as OWC.

To start your iMac in Target Disk Mode hold the t key while starting it. Be aware of the effects of migrating potentially incompatible software as the others mentioned. Documents and similar data won't be a problem but newer software may require their file formats to be updated, which is typically not reversible.

Can I take my backup drive from the old computer and plug it into the new IMac and download files from Time Machine?

Probably. There is no harm in attempting to do so. Choose "From a Time Machine backup or other disk" as explained earlier.

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Salix wrote:

 

... Do I use a Firewire cable with adapter or a Thunderbolt cable with Firewire adapter?

You can use either one. Since you already bought a cable all that is required is a Thunderbolt to FireWire adapter. There may be sources other than Apple but that's the one I use.