Is it bad or is a Ps4 game like COD running on a 144hz monitor?

I recently bought a monitor with 144hz and have often seen on the internet that it would not run because the PS4 only has 60fps anyway. However, this monitor was intended for the PS5 I'm already looking forward to. Apparently it should have 120fps.

Hence my question whether the PS5 would run at a presumed 120fps on my 144hz monitor?

Yes she would

Thanks for your quick reply.

Would run, but you have nothing of the 144hz because the game on the ps4 only runs at 60fps.

The Ps4 only runs at a maximum of 60fps anyway. Although it is still not a problem to gamble with a 144hz monitor, it is worth it is another matter