my eMac cannot run OS X Lion v10.7.5 or later and iPhoto 9.2.2 or Aperture 3.2.3 or later; how do i get the photos from my iPhone 5s saved to my eMac?

Only way I know would be to eMail them to yourself on the eMac, which would be a pain if there are a lot.

Or do you have a later Mac that could get the photos & File Share with the eMac?

Turns out it may be possible...

https://discussions.apple.com/thread/6472306

Leopard requirements/10.5.x...

* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor

minimum system requirements

* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)

* DVD drive for installation

* 9GB of available disk space (I say 30GB at least)

Classic/OS9 Apps no longer supported.

Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...

http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5

There are workarounds if the 867MHz CPU is the only hangup...

http://sourceforge.net/projects/leopardassist/

http://lowendmac.com/osx/leopard/unsupported.html

Then you'd need iLife 09.