Is it normal or even possible for a girl to ovulate 5 days before her next period starts?

Ovulatipn. I think anything is possible, just about. It would mean that the "looking face" is extremely short and she is making very little or no progesterone. More than likely what is happening is she is having luquillo phase leading caused by a polyp or some other endometrial pathology. Perhaps a fibroid. I would start with an ultrasound.