using an iMac 2017 27 inch 5k as a display for a mac mini late 2014

no,

Use your iMac as a display - Apple Support

Note: Target Display Mode isn’t supported on iMac models with Retina display. Only iMac (27-inch, Late 2009), iMac (27-inch, Mid 2010), and iMac (Mid 2011 to Mid 2014) support Target Display Mode.

The last iMac that supported Target Display mode was the early 2014.

As a matter of fact, any iMac, even those Target Display capable, that

are running Mojave or Catalina do not support target display mode.

BTW, the iMac is a computer and not a display.

The only alternative is to use Screen Sharing via ethernet (WiFi

will ten to be too laggy) or use some other VNC client/server

app. Also, depending on the applications you are using, this

may not even work that well.

If you really wan't a display for the Mini, buy one.

there are third party software which make do it but then it's wireless and if something goes wrong one would likely have to connect a monitor to the mini to resolve it.

the reason it worked for the older ones is likely their have lower resolutions, using target display mode from a mac which does not support the 4k and 5k resolutions would mean the imacs would not be running their native resolutions, and lcd which does not run their native resolution or a modulus 2 of their native resolution would look fuzzy.