Can’t update to Monterey or Ventura.

Hello M0nk60,

For iMac (Retina 5K, 27-inch, Late 2014), macOS Big Sur is the latest compatible operating system. Other models of iMac (Retina 5K, 27-inch) are compatible with either macOS Monterey or macOS Ventura. This resource has more details, for reference: Identify your iMac model

If you have a compatible model, let's use the steps below to boot into safe mode to see if that persists from there:

1. Turn on or restart your Mac, then immediately press and hold the Shift key as your Mac starts up.

2. Release the key when you see the login window, then log in to your Mac. 

3. You might be asked to log in again. On either the first or second login window, you should see ”Safe Boot” in the upper-right corner of the window.

You can also find those steps in this resource: How to use safe mode on your Mac

It can take a few extra minutes to boot into safe mode. Your screen may flash or flicker while in safe mode. Those behaviors are expected. Testing in safe mode runs a check on your disk, removes some cached files, and can help isolate conflicts with startup items. Once you've tested that behavior in safe mode, you can restart to leave safe mode.

Should that still persist in safe mode, do you get any errors or prompts when you attempt to upgrade macOS?

Let us know, and we'll keep moving forward based on your results.

Ah! A solid clue!

...started it in safe mode and the message reading Installer is damaged.

That poorly-worded alert only means the current installer found an older, outdated version of itself in your Applications folder. Find and delete it, and your should be able to successfully upgrade.

M0nk60,

Based on the troubleshooting you've already tried we'd encourage you to reach out for additional support here: Get Support

Take care.