Q: What is the most effective way to get my imac 2 ghz intel core duo 2 10.4.11 to be able to run 10.5 and sync with my iphone 4s?

As your Mac should run Snow Leopard provided it has at least 1GB memory, that would be a good deal easier and very much cheaper than trying to find a 10.5 install disc.

Snow Leopard costs $30 approx from the online Apple store (£26 if you're in UK)

You'll need to update Tiger to 10.4.11 with the combo installer first (unless you're just erasing the disc and starting fresh) You can then update SL from 10.6.3 to 10.6.8 with its combo installer.

For comparison, 10.5 Leopard is currently running about $130 from Apple (if still available) and more on Amazon etc.

This info for Leopard courtesy of TexasMacMan;

Mac OS X 10.5 Leopard installation system requirements

http://support.apple.com/kb/TA24950

Leopard is no longer available at the Apple Store but may be available by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753).

If you can't obtain a retail install DVD from Apple, look on eBay or Google the installer part numbers to possibly find at an on-line store. Here's what to look for:

MB427Z/A  Leopard 10.5.1 install DVD

MB576Z/A  Leopard 10.5.4 install DVD

MB021Z/A  Leopard 10.5.6 install DVD (single user)

MB022Z/A  Leopard 10.5.6 install DVD (5-user family pack)

Installing Mac OS X 10.5 Leopard

http://support.apple.com/kb/HT1544

Mac OS X 10.5 Leopard Installation and Setup Guide

http://manuals.info.apple.com/en/leopard_install-setup.pdf

After you install the base 10.5, download & install the 10.5.8 combo update at http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update