Can I install macOS 13 on a Mac older than 2017?

No.

macOS Ventura is compatible with these computers - Apple Support

If you have a 27" iMac that is running Monterey now (as indicated by your tag line), that would imply that it is a Late 2015 model for which the end of the line is Monterey. If it had been from Mid 2015 or earlier, it wouldn't have been possible to upgrade it that far.

No.

(258351)

Yes - but only via a VM (virtual machine) : you'd have to run this alongside your current OS so you'd need maximum RAM to support both. However if you allocate minimum RAM to your current OS and the rest to your VM you could spend most of your time and activity in the VM, having moved your apps to it.

christopher rigby1 wrote:

Yes - but only via a VM (virtual machine)

You cannot run a macOS VM that is not supported by the host Mac.

dialabrain wrote:

You cannot run a macOS VM that is not supported by the host Mac.

My mistake - I read the OP and somehow my mind read 10.13 instead of just 13.