Your doctor, no one, can positively tell when you actually conceived. All dates are approximations.
If your last period STARTED on 11/22 then you had sex on day 8 with your "close friend."
You then thad sex with your "former boyfriend" on day 8 and 13.
You don't necessarily get pregnant the day you ovulate. It can take several days. Sperm can also survive for about 5 days while your egg, about 48 hours.
Normally you'll ovulate between days 11 and 16 of your cycle or 12/3 to 12/8. Odds strongly favor your 12/5 partner as being the father. There is always a chance, however slight, that your close friend is.
A DNA test can confirm paternity.
Hope it helps.