The effect on appearance depends on the type of surgery and its purpose. If the surgery only involves one of the two jaw bones, a 5 mm advancement will have a significant effect on facial physiognomy.
In the case of sleep apnea treatment, orthognathic surgery simultaneously affects both jaws. If the relationship between the two jaws is adequate, apnea correction will generally require an advancement ranging from 10 to 12mm. With such advancement, we can see a noticeable effect on the physiognomy, but altogether it remains harmonious and any change will appear modest. You should also know if tissues are soft and large (thick lips and cheeks, round face, slightly overweight), changes are less obvious. When the required advancement is more than 12mm, it becomes difficult or impossible to move the jaw without causing significant changes in physiognomy. These can even become unesthetic.
If you have concerns about physiognomic changes, please discuss this with your surgeon. He will tell you more about the effects of surgery.