Using a late 2014 iMac 5K retina display as an external monitor for a new MacMini

Sorry, but the iMac cannot be use as a monitor for any new Mac, nor PC.

This is no longer supported by Apple in the macOS nor in hardware.

Apple killed target display mode hardware when the first Retina Macs were released in 2014 and died in software with the release of macOS 11 Big Sur.

There would be no advantage to using that old iMac even if it could be used. The power consumption of a computer versus that of a dedicate monitor is much higher. There are more components that might fail at any time as it's already nearly eleven years old. The cabling alone could cost nearly as much as a low end monitor.

Just plan to add the cost of a monitor to that of a mini. You'll still come out ahead even if you spend $300-$400 for a nice monitor.

Please see this guidance on the subject:

Using an iMac As A Monitor

(Thank you, John Galt)

All of the 27" 5K Retina iMacs have very good screens. When Apple discontinued the 27" 5K Retina iMacs in favor of a standalone 27" 5K Studio Display, they priced that display very high by 27" 5K iMac standards – and initially, there were no competing 27" 5K displays except one made by LG.

These are some of the reasons why Mac users are so interested in using 27" 5K Retina iMacs as displays for new Macs. Unfortunately, none of those iMacs support Target Display Mode. That feature went away when the first 27" 5K Retina iMac came out in Late 2014. Apple later added restrictions on newer Macs and versions of macOS that mean that none of them even support using older, non-Retina iMacs as Target Displays.

There is a workaround product, called Luna Display, that might let you use a 27" 5K iMac as a second screen. You will still need at least one real hardware display. An article on Astropad's site acknowledges that their product has limitations and is not recommended for high-motion content.

Fortunately, we are finally starting to see more selection in 27" 5K displays. You can currently get, or will soon be able to get, 27" 5K (5120x2880 pixel) displays from Apple, LG, Samsung, Asus, BenQ, and ViewSonic.

If you can settle for a 27" 4K monitor, some of those with IPS panels and 100% or near-100% coverage of sRGB go for as little as $300 – $350. But you will give up some sharpness.

No new Mac's from 2019 on including the Mac mini, support using an iMac as a display in Target Display Mode.

carefully read > Use your iMac as a display with target display mode - Apple Support

If you have or get a new Mac mini, the you will need an external display to use as the primary display.

see > Connect a display to Mac mini - Apple Support