Q: How to upgrade imac os from 10.4.11 to 10.5 or later?

You purchase Mac OS X 10.5 on DVD(or 10.6 if you have an Intel Mac) and back up everything before installing it.

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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)

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

List of Applications Not Compatible with Leopard...

http://guides.macrumors.com/List:Applications_Not_Compatible_with_Leopard

Snow Leopard/10.6.x Requirements...

General requirements

   * Mac computer with an Intel processor

    * 1GB of memory (I say 2GB at least)

    * 5GB of available disk space (I say 30GB at least)

    * DVD drive for installation

    * Some features require a compatible Internet service provider; fees may apply.

    * Some features require Apple’s MobileMe service; fees and terms apply.

Which apps work with Mac OS X 10.6?...

http://snowleopard.wikidot.com/

It looks like they might still have it...

http://store.apple.com/us/product/MC573Z/A?fnode=MTY1NDAzOA

If it's a Core Duo & not a Core2Duo, then it'll only run in 32 bit mode.

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

The DVD should look like this

Caution - Leopard does not support classic mode. So, if you currently open OS 9 apps in classic mode, you won't be able to do this if you upgrade to Leopard.

 Cheers, Tom