My computer is 10.4.11 - can i upgrade to OSX 10.10.5?

I doubt it, my guess is the best you can do is Lion, but to check, hold down the Option key and select System Profiler from the Apple Menu.

The hardware section should be selected. Look for model Identifier. It will be something like imac3,2. Post that and we can determine for sure.

Check that your computer is compatible with Mountain Lion/Mavericks/Yosemite/El Capitan.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

• iMac (Mid 2007 or newer) model number 7,1 or higher
• MacBook (Late 2008 Aluminum, or Early 2009 or newer) model number 5,1 or higher
• MacBook Pro (Mid/Late 2007 or newer) model number 3,1 or higher
• MacBook Air (Late 2008 or newer) model number 2,1 or higher
• Mac mini (Early 2009 or newer) model number 3,1 or higher
• Mac Pro (Early 2008 or newer) model number 3,1 or higher
• Xserve (Early 2009) model number 3,1 or higher

Your Mac needs:

• OS X v10.6.8 or OS X Lion already installed
• 2 GB or more of memory (More is better - 4 GB minimum seems to be the consensus)
• 8 GB or more of available space

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.

Application Compatibility

Applications Compatibility (2)