5 1/8'' is 5.125 this pocket is precisely 5.25. This photo was provided by Jayson after his record run.
If I zoom in on this photo on my monitor, then the two balls are 14.4 cm and pocket corner to corner is 16.8 cm. So no matter what your monitor and resolution, the pocket is 168/144 times bigger then the 2 balls. Since diameter of an aramith ball is exactly 2 1/4 '' this picture corresponds to exactly 5 1/4'' pockets (and 139° angle of the cushions)
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I'm very familiar with the OpenCV algorithms used by that website and you will get radically different distance measurements when you have minor offsets in camera angle and attitude. You could experiment with your own pockets and see how estimated distances vary with small movements in the camera.
I defer to the experts as to the actual size of these pockets or if any of it matters. The live stream was awesome at least.