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Hi, It's Dr. C. Thanks for asking for me.
Because the doctor was so specific, saying 6w5d, it sounds like it was from an ultrasound that he/she determined the gestational age.
If so, the most likely range for conception is May 21 to June 6 with peak most likely day being June 3rd.
It helps that the someone else was after that because sperm can live for 3-5 days, so if the someone else was before, it would be trickier. Because the sperm could be present several days after.
First trimester ultrasounds are the most accurate way of determining conception date. So although these dates are pretty close, because the boyfriend was before it seems highly likely that he is the father. I don't think I can say 100% sure but pretty darn close to that.
I hope this was helpful. Please reply if I can clarify anything.