Mac Pro 5.1 late 2012 stopped working with cinema screen.

your Mac Pro 2012 does not have Thunderbolt-2 ports, or USB-C,

Cinema display LED 27-in A1316 from 2011 is a 2560 by 1440 display that features lead-in cord with three connectors -- Mini DisplayPort, MagSafe-2 and a USB-A pigtail. It does NOT work with the Thunderbolt adapter, but works fine with a USB-C to miniDisplayPort adapter.

It includes three USB 2.0 ports and a convenient single cable with THREE connectors (Mini DisplayPort, MagSafe-2, and USB 2.0), a built-in iSight camera with a mic and a 2.1 speaker system.

This display works great with a USB-C to MINI-DisplayPort adapter.

For use with older Macs like your Mac Pro 2012, you might be using no adapter, or a DisplayPort to Mini DisplayPort adapter. (depending on what card you are using.)

from:

https://everymac.com/monitors/apple/studio_cinema/specs/apple-led-cinema-display-27-inch-specs.html

That's the case I described above.

The Mac 5770 has two Mini DisplayPorts.

Before you pull everything apart to connect to a MacBook Pro, try the other mini DisplayPort. I have seen one port on a graphics card fail and the others continue to work.

I see that there are several others that might be called cinema display, including the 30-in Cinema Display that I use. these would use different connection methods.

¿Which is your display?

what graphics card are you running?