You should find these calibration notes helpful: https://tlfong01.blog/2019/04/26/ph-4502c-ph-meter-calibration-notes/
The Arduino does not measure absolute voltages. It measures voltage relative to its power supply voltage. That is never exactly 5.0 V, although your program assumes that to be the case.
You need a multimeter to measure voltages with reasonable accuracy.
You are correct that the adjustment should allow a wider range than you observe. I suspect that there is something wrong with your setup, but you have not given enough details to guess what that might be.