Apple Cinema Display went black

Do you have anything connected to the built-in HDMI port? a display or a sound system?

Presuming you do NOT,

your Mac is rated to support that one 5K display over its built-in Thunderbolt-4 ports using the display-supplied cable.

It is intended to support that display at up to 120 Hz or variable refresh rate over, HOWEVER:

Users are finding that apparent Bugs in MacOS result in occasional kernel panics, and the display is MUCH more stable when set to 60 Hz refresh rate.

If you are offered a firmware update for that display, it should definitely be installed to improve performance.

What cable are you using to connect?

What device (which Mac model, exactly) are you connecting to?

is your cable plugged into the display's port closet to the stand, not farther away?

so MacBook Pro... what model year is that exactly?

¿What processor (Intel, M1, M2, M3, M4, M5, something else) ?? and what suffix {(plain), PRO, MAX, ULTRA} ??

I ask this because it determines how many and what kind of displays can be supported in which ways.

The last Apple Cinema Display was discontinued in July 2000. it seems unlikely you would refer to that as your "new" Apple display.

¿What EXACT model display are you using?