Using a 2019 27” iMac as a Display for Mac Mini

Unfortunately, that setup is not supported by Apple. The iMac cannot be used as a monitor for any of the newest Macs and Target Display mode is no longer a feature of macOS, having been deprecated several years ago.

Please see: Use your iMac as a display with target display mode - Apple Support

Per the link above:

• Your target iMac (monitor) must be using macOS High Sierra 10.13.6 or earlier. 

• In all cases the source Mac that you're connecting FROM must have been introduced in 2019 or earlier and have macOS 10.15 Catalina or earlier installed.

However, you might consider a third-party solution, for example: Luna Display or Duet Display, though I can’t speak for the performance of those.

Do yourself a favor, avoid the headache and just budget an extra $100 for a monitor. Yes, they are that inexpensive.

That iMac is new enough that you could use it as an AirPlay Receiver for AirPlay to Mac.

System requirements for Continuity features on Apple devices - Apple Support

Set up your Mac to be an AirPlay Receiver - Apple Support

This would be as an extra display, since you'd need at least one real display to set up the feature. I don't think that AirPlay would support the full 5K resolution of the display, and there might be other video quality issues.

But it would be free to experiment with, if you already had the Macs.