Can you get pregant the day before you period?

Patient: Earlier this month I started taking birth control for the first time. I was almost done with the pack with one week left but I left it at home while I was on vacation, I missed five pills all together. Then I had unprotected sex this Tuesday, Wednesday and Thursday. I also started my period on Thursday. How worried should I be that I am pregnant?

Symptoms: None as of right now. My flow on my period is pretty heavy.