Another concieving/conception question..

Due May 8th according to ultrasound and I must be getting annoying with these questions, so my concern is if I had sex on September 8th i would have been 5 weeks and some days pregnant, correct? It's impossible that I conceived on September 8th if my ultrasound says I'm due May 8th? I didn't get my periods so I wouldn't know the exact date, and it's impossible to conceive at 5 weeks right? I'm only concerned because my ex and I had broken up before September and I been with one guy on September 8th and found out I was pregnant two weeks after that, and at my ultrasound I was 9 weeks and 3 days, I've asked my doctor but she wasn't helpful I think she was new as well because she couldn't even find the baby's heartbeat, so I'll ask again with a different doctor at my appointment tomorrow, I just don't wanna feel judged..