It is possible, but highly unlikely. It is not unheard of for women to get pregnant at various times in their cycles, including during their period. It is also not unheard of for women to have periods while pregnant, especially the first month. However, this is not the norm. Most of the time ovulation occurs midway through your cycle. Thus if your cycle is 28 days, you would ovulate 14 days after the date you start your period. If you had sex five days before that time to a day or two after that time, you would have a good chance of getting pregnant (if your system and his were both working properly). It is not likely that you are pregnant. If you have symptoms of pregnancy and think you might be pregnant, I would recommend a blood test a couple weeks after the unprotected sex you think would have resulted in the pregnancy.
No, it's not likely as you don't ovulate the day before your period.