How can I tether my Canon 5D (original) to an Apple computer running the High Sierra OS?

According to this document you can use Lightroom to tether Canon EOS 5D.

Based on the version you can buy and use even a perpetual license (Lightroom 6). Here is link in Amazon (currently not available)

Lightroom (Classic - as the desktop version is called nowadays) should support the Canon 5D since Version 3. I am not aware that the support was ever revoked.

https://helpx.adobe.com/lightroom-classic/kb/tethered-camera-support.html

Capture One Pro indeed does no longer support it.

https://www.captureone.com/en/resources/tech-specs/camera-support-canon

There are two distinct versions of Canon's EOS Utility. Cameras older than around 2012-14 use EOS Utility 2.x.xx, while cameras since that time use EOS Utility 3.x.xx. EOS cameras released in the period around 2012-14 are compatible with either version. Both versions can be installed simultaneously on the same computer. If a camera from the "overlap" period is connected, EOS Utility 3 will be used by default for that camera, but if only EOS Utility 2 is installed, those cameras will work with it as well.

It seems the last Mac OS that Canon shows with a version of of EOS Utility available at the 5D support page is EOS Utility 2.7.2 for the original version of Mac OS X. When one looks at the support page for the EOS 5D Mark II with Mac High Sierra v10.13 selected as the OS, however, it lists EOS Utility 2.14.31c for Mac OS X in the available downloads, which indicates that version should run on High Sierra v10.13. Unfortunately the oldest EOS cameras supported by that version of EOS Utility 2 were introduced in 2007 or later. The list doesn't quite go back all the way to the original 5D from 2005.

If you haven't done so already, you might try downloading EOS Utility 2.7.2 from the 5D Mark II support page. You'll need to manually enter Mac OS X as the operating system in the dropdown menu on the 5D Mark II support page for it to display in the list of downloads. You'll also need an original Canon Utilities CD with an earlier version of EOS Utility 2 on it and a way for your Mac computer to read it in order to use the "updater" which is actually the full program that requires a previously existing version installed or an appropriate Canon Utilities CD in an optical drive at the time of installation.

Sigh.

What some folks have been known to do when dealing with similar issues around older devices is to use a dedicated legacy computer running an older OS that is compatible with the last versions of software compatible with the device. Of course when running such old legacy systems, they should be configured to not be connected to the internet for obvious security issues. I've got an old Windows XP machine that I use with an older high end sound card which has an external box with various specialized connectors that I use with analog audio production equipment. I use the XP machine as a digital capture device. Once the files are digitally captured, I can transfer them to my newer computers using external hard drives without risking connecting the XP machine to my internet connected network.