Can I upgrade the system on my iMac OS X Yosemite version 10.10.5 to a newer system

As den.thed posted, the macOS version you can upgrade to depends on the year model of your Mac.

Check the Compatibility of your Mac with these newer versions of macOS:

➡️ macOS 10.13 High Sierra is compatible with the Macs listed here

➡️ macOS 10.14 Mojave is compatible with the Macs listed here

➡️ macOS 10.15 Catalina is compatible with the Macs listed here

➡️ macOS 11 Big Sur is compatible with the Macs listed here

Upgrading the OS X, depends on the year model.

see > Identify your iMac model - Apple Support

Once you determine which iMac you have, and what versions of Mac OS X / macOS are compatible with it, your next task is probably going to be getting hold of an old version of macOS.

By default, the App Store only shows the latest version (currently Ventura) – hiding all others. But you can some of the others by going through this Apple Support page:

How to download macOS - Apple Support

Which exact Mac do you have. Apple logo at top left>About this Mac…