Can I hook up a 2015 iMac to a Mac Mini? If not, what would you suggest to me in this situation?

Sorry no, none of the new Mac's including the Mac mini support the old Target Display Mode requirements.

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

Most any aftermarket USB-C, HDMI, DisplayPort display or DVI, VGA monitor will work with the Mac mini.

see > Connect a display to Mac mini - Apple Support

Hi, arden193, maybe I can help you.. your idea of hooking a new Mac mini up to your 2015 iMac that’s running slow and generally dying won’t work as Target Display Mode hasn’t been supported for 10 years or so… I’d suggest getting and using an external hard drive/SSD with roughly the same capacity/storage space as your 2015 iMac , if not somewhat larger. USB 3 should be just fine for that, unless you can find a good deal on a Thunderbolt 2 equipped hard drive/SSD… then, assuming your iMac is still functional, shut it down, plug in the external hard drive/SSD to your iMac, plug in its power cable and restart your iMac… hold down the “D” key on startup, that should get you Apple Diagnostics… and you can confirm if your internal hard drive/SSD is going bad…,if it is, use Disc Utility to Mac format to the external drive( if it isn’t already) then turn on Time Machine, point Time Machine to the external drive, say you want to use it as a backup drive and do a backup of your iMac. Time Machine is reliable. Ez to set up and use, and almost automatic… and it’s a smart thing to do and use… as for a good external monitor, I can’t say… it depends on your budget for such a thing, and how big you want it to be, and if you

want it to do 4K or 5k… shoot, with a usb-c ( thunderbolt 3) to hdmi 2.0 cable you can use a regular hdmi tv as a monitor…

john b