is there a way to update the Yosemite operating system 10.10.5 updated to 10.11.6

Hi there!

Yes, you can upgrade from OS X Yosemite to OS X El Capitan. To begin, visit the Apple Support article How to download and install macOS - Apple Support, and under the "use a web browser" section, choose El Capitan 10.11. This will download an installer, placed in your Downloads folder, to install the OS X El Capitan installer application. Open it, and follow the on-screen steps to install the application. After it's installed, you can open the app "Install OS X El Capitan" from the Applications folder in Finder, or Launchpad, and begin the upgrade.

Before installing new software, it's a good idea to back up your Mac.

Jack

It could very well be.

No. 10.11.6 is the latest version you can run.

An Early 2009 24" iMac can run 10.11.6 El Capitan.

see > Identify your iMac model - Apple Support

To upgrade, use the directions at > How to download and install macOS - Apple Support

I could be mistaken but the way I read the question, it's already running 10.11.6 and was inquiring whether it could be upgraded further.