Can I use an iMac Retina 5k as a display for a new Mac Mini M4 chip?

You cannot.

There are third-party options such as Luna Display or Duet Display, but these are performance limited and suited only for uses where there will be limited motion and where lag time is not an issue, such as for application tool palettes.

Please also see this recent thread for another option using screen sharing.

Using iMac as monitor for Mac mini via Sc… - Apple Community

And you still will need a proper monitor to set up any of these options.

In addition, an iMac will use much more power than a proper monitor in daily use. So there's that.

Nope, you need to buy an external display for the MM. They begin at <$100 and do not require expensive cabling. You can also spend as much as $1500 however for about $300 you can find a very nice display.

Also, a much better solution than using software which can be expensive, needs updating (additional costs??), complex and potentially unreliable.

That iMac doesn’t support Target Display Mode. That feature went away when the first 27” 5K Retina iMac (yours) came out.

Apple also added restrictions on the video source, such that no current Mac supports using any iMac as a Target Display.

No.

The M4 Mac mini does not support Target Display Mode.