I have a 2005 iMac with a mini display port and a 2021 MacBook Pro with a hdmi port. How do I connect the two together?

Why do you want to connect them together?

You can't because the 2021 MacBook is too new. Target Display Mode was dropped several years ago. Only older Macs can use it.

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

Sorry, but that will not work because neither of those models support Target Display Mode.

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