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

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.

It could very well be.