Can I use iMac 27" late 2015 as display for 2024 Mac Mini M4?

Nope, you need to buy an external display. Please remember that iMacs are computers, they are NOT external displays for other devices. You can read up on Target Display Mode (that died 10 years ago) in Target Display Mode.

Your iMac does not support Target Display Mode. No Retina iMac does. Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014, and never came back.

Apple also added restrictions on the video source which mean that the M4 and M4 Pro Mac minis are unable to use any iMac as a Target Display.

See the bad news here: Use your iMac as a display with target display mode - Apple Support

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Your iMac is too old to be an AirPlay Receiver for AirPlay to Mac. There are third-party applications which might let you turn that iMac into an AirPlay display, but I believe you'd be able to select a resolution of at most 1920x1080 … so you wouldn't get the benefit of that nice 5K display, and on top of that, there could be lags and artifacts.

See the bad news here: Continuity features and requirements for Apple devices - Apple Support

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There is a third-party workaround product called Luna Display that might let you use that iMac as a second display, with limitations.

Astropad – Luna Display

Astropad – Use Your iMac as a Monitor: A Step-by-Step Guide [2024]

"Like any product, Luna Display does have limitations and it’s not recommended for high-motion content. For example, I wouldn’t recommend using Luna Display for gaming or video editing.

Since Luna Display is squeezing a 5K display through a USB cable, when lots of motion occurs on-screen (like from video playback or moving a window quickly) the screen can temporarily become pixelated before it renders in at full resolution."

[Boldface is theirs.]

Even if these limitations are acceptable to you, I think you'll still need a real hardware monitor to set up Luna Display, and you will still want to have a real hardware monitor in addition to the iMac.

As far as a standalone monitor that has a similar screen to your 27" 5K iMac, there's this:

Studio Display - Apple

There are also a couple of 27" 5120x2880 pixel monitors from LG and Samsung. They, too, list for well over $1000, but those two can often be found on sale for street prices of $800 – $900. I don't know how well they compare to the Apple one.

Not without using a standalone monitor to set up Virtual Network Computing.

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