Upgrade graphics card on my Mac Pro 5.1. it has Apple Cinema Display 27” / Model A316

The model identifier "MacPro5,1" matches

• Mac Pro (Mid 2010)
• Mac Pro Server (Mid 2010)
• Mac Pro (Mid 2012)
• Mac Pro Server (Mid 2012)

Identify your Mac Pro model - Apple Support

You can upgrade all of these machines as far as Mojave – if you have a recommended Metal-capable graphics card. You cannot upgrade any of these machines to Catalina or later.

The graphics cards that you saw might be compatible with "Monterey, Sonoma, and Ventura" if installed into a Mac Pro (2019), but putting one of them into your Mac Pro will not let it run any of those versions of macOS.

Those two cables supply POWER for the increased needs of the more modern card.

PCIe describes the data Bus connections on the backplane -- you can't get that in parallel form into an ordinary cable.

Whatever the labels on the switch say, do not depend on their meaning. the rule is simple: if one setting does not work, just keep, track of what you tried and check the other setting.

Any card you install must feature "Boot Screens" -- the ability to view the boot picker, Recovery, installer, and login screens.

You can use PC Cards, PROVIDED their firmware has been flashed to support Mac Boot screens. This is not trivial, and a seller will know and feature Boot screens prominently in their ads.

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Any card with a DisplyPort output can drive your display through a simple "just wires" adapter from [full size] DisplayPort to [mini] DisplayPort.

The Saphire Radeon HD 7950 (Mac Edition) is the most directly upgrade and comes with mini DisplayPort output, but those are admittedly old cards. As previously mentioned you can use a full size DisplayPort to mini DisplayPort cable with a newer graphics card such as an RX 570 or 580.

I would caution against a nitro+ special edition. It probably will work, but some cards that require 6+8 pin power connectors have had power instabilities when installed in a 5,1. A different RX 580 card that only requires a single 1x 8-pin power connector would be a safer bet when using a dual mini-6pin to 8-pin adapter cable.

if you get a picture (including boot screens) with the switch setting you have now, you are done. The other setting can't be better.