If you want Snow Leopard or later you need an Intel Mac.
If Apple menu -> About This Mac says PowerPC G4 or G5, you can't upgrade to Mac OS X 10.6 or later, and
you can't sync with iOS 6 or later. Upgrading to 10.5.8 from 10.5 is possible, and is explained on:
If Apple menu -> About This Mac says Intel CoreSolo or CoreDuo you can only upgrade as far as 10.6.8.
https://discussions.apple.com/docs/DOC-2455 explains how.
You do not need Leopard to get to Snow Leopard.
If Apple menu -> About This Mac says Intel Core2Duo, i3, i5, i7 or Xeon, you can upgrade to at least 10.7, but have to be careful about compatibility with Rosetta, as this tip explains:
You do not need Snow Leopard to get to Lion on an empty hard drive if you have the USB Flash drive of Lion (10.7).
You do need 10.6.8 or later to install 10.8 or later.
For more limitations of Lion, see this tip:
10.5.8 is the most current operating system if you have a PowerPC G4 867 Mhz (G4 800 Mhz dual processor can't natively support 10.5 or later)
or 1 Ghz or faster, or PowerPC G5. 10.5 does not support Classic, but does support dual booting into Mac OS 9.
10.5 is the minimum for Intel Macs to support Boot Camp, the Windows virtualization engine.
No G5 is an Intel, and no Intel is a G5.