Most doctors are pretty useless when it comes to running injuries. They give you a quick diagnosis and then push you out the door to let the passage of time do their job for them.
Five stress fractures is rough. What this undoubtedly proves is that your kid tolerated the pain too well. Your kid decided to be strong rather than listen to his body. This is easy to do in an environment where everyone wants you to do a lot of running and you would look lazy if you did not.
He needs to cease all running for 3 months. He should not return until he has zero pain. Stress fractures are usually a repetitive stress injury, which means they get worse the more you run on them. Your kid ran on them in pain before and they got worse. He needs to start from a point of zero pain to ensure they are not present and do not get worse.
When he returns to running in a few months he should try to start with walking and jogging in grass and then slowly build up from there. The walk/jog phase could take weeks or a month and you don't really want to progress to running until he's sure he has no pain. Well manicured grass is his friend, as are shoes that are neither too soft nor too stiff.
From then on out he needs to listen to his body. Running is a sport of stress and adaptation. You stress your body and it responds. If you stress it too much then the response is often injury.
Lastly make sure the kid is eating plenty of food. Stress fractures to that extend can often be the result of malnutrition, such as not enough calories or calories with no nutrient content.