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Yes you can upgrade it but it is not straight forward.
The process is as follows
You can upgrade your machine to the newest version of the OS, Yosemite (OS 10.10.0), which just came out. But, you first need to upgrade your machine to Snow Leopard, OS 10.6.0, and then to OS 10.6.8. Here is an explanation that explains how to do all that:
"Upgrading to Snow Leopard
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mavericks if your computer meets the requirements.
Snow Leopard General Requirements
1. Mac computer with an Intel processor
2. 1GB of memory
3. 5GB of available disk space
4. DVD drive for installation
5. Some features require a compatible Internet service provider;
fees may apply.
6. Some features require Apple’s iCloud services; fees and
In order to upgrade to Mavericks (OS 10.9.5) or Yosemite (OS 10.10.0), you will need to increase your memory, to at least 2GB. Depending on what type of processing you do with your iMac, you should consider upgrading the Ram to at least 4 Gig, and if you want, you can upgrade to its' maximum, 6 gig.
Once the RAM upgrade has been completed, you can then upgrade from Snow Leopard, OS 10.6.8, to Yosemite, OS 10.10.0. Here is the information about doing that:https://www.apple.com/osx/how-to-upgrade/
One thing you MUST do for the first upgrade, from OS 10.5.8 to OS 10.6.0 to 10.6.8, is to FIRST make a backup of your OS 10.5.8 "system". You can use the "freeware", earlier version of SuperDuper! (download link Click me to view
Once that is done, and everything is OK, perform the upgrade from 10.5.8 to 10.6.8, as described above.
Next, you will need to backup the OS 10.6.8 "version" of your system. You can use the newest version of SuperDuper for that (download link http://www.macupdate.com/app/mac/13803/superduper
Once that is done, and OS 10.6.8 is running fine, you can then upgrade to Yosemite.
Finally, you will need to insure that all your third party applications are first compatible with Snow Leopard (OS 10.6.8), and then with Yosemite (OS 10.10.0), if you decide to go that far.
So as stated, it can be done but is quite a bit of work.
If you would like any additional information or assistance, please do not hesitate to let me know.
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