How long does one 5cm large liver cancer tumor grow to spread? Doctor suggested surgery but dad wants to know how long can he wait before surgery?

Don't wait. Length of time depends on the proximity of the cancer to structures that would allow it to spread. Your oncologist and surgeon can give an estimate, but it is not usually beneficial to wait with a cancer. .
Well... the smaller the tumor the better the chances at a cure... the sooner the better.