Normally the fertile days are around ovulation which usually occurs 14 days before the first day of your period. In general, the fertile period in a cycle starts from the number of day calculated by shortest cycle minus 18 days and ends on the number of day calculated by longest cycle minus 11 days. So, if your shortest cycle is 28 days and longest is 35 days, your fertile days in a cycle can vary from (28-18) = 10th day to (35-11) = 24th day, where first day of your cycle is the first day of your period.
But that is not a hard and fast rule and a lot depends on the regularity of your cycle. That being said, in your case, it is a possibility that if you had sex around 30th or 31st May, even though it was last day of your period, the sperms may have been able to survive till the time you ovulate. I am assuming that you must have had a TVS (sonogram) that confirmed your dates. Usually the first trimester ultrasound
is very reliable in terms of dating. So if it says that your are 5 weeks and 1 day pregnant (the first day being the first day of your LMP) today, Jul 8th, it is less likely to go as far back as 19th may for your conception day. Hence, my best guess is that you may have conceived somewhere in the month of June (probably 2nd or 3rd week of June). If you have more doubt, it would be a good idea to discuss this with your OBGYN
who did your sonogram and she will be able to provide you with more details.
Hope that helps.
Take care and all the best for your pregnancy