More than 6 years later - now running Mojave 10.14. Dark Mode makes the upgrade worth it.

http://dosdude1.com/mojave/

This 2010 iMac (11,3) built in video card is *NOT* Metal compatible so video acceleration is DISABLED with Mojave which makes your iMac screen refresh sluggish, Photos to go black and other graphics anomalies but everything else is stellar.

However... Don’t install Mojave or Catalina on this machine. It will barely run and the experience is terrible. This quote is from DosDude1 himself: “Radeon HD 5xxx and 6xxx series video cards are not, and most likely never will be, supported under Mojave or later.“

After Mojave installation, your colours will be inverted. To fix - Go to System/Library/Extensions and put this file into the trash: AMDRadeonX3000.kext then reboot