How To Calculate The Exact Date Of Conception?

I have a bf and we have unprotected sex.My last perios was FEB22/23. I had sex with someone else on May 8th and took plan b within 12 hours. I found out I was pregnant on May 29, and based off of my persiod was told i was 5 weeks pregnant. I got an ultrasound on APRIL 10th , and was told I was 7w4d. Is it definite that I was pregnant before I had sex on May 8th, and the ultrasound was correct?