Difficult Upgrade to 10.5

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do you have another Mac? use FireWire target disk mode

EDIT: you can do it both ways: boot the Mini in FWTDM (holt down T as it boots) and hook up to another Intel Mac with good optical drive and install from there, as the Mini were a simple external Hard Drive

Or you can put the 10.5 DVD in the other mac with good optical drive, boot that in FWTDM and hook up to the mini, and both HD and Optical drive should show up on the Mini. Eject the other HD so you don't mess with it, and use only the optical drive as if it were an external FW optical drive