Hi Ashr, I doubt that you had an ultrasound this early. The Aug 27th date of ovulation and thus conception was obtained by adding the standard 14 days to your Aug 13 LMP. Since sperm are said to survive inside no more than 5 days, the Aug 24th encounter was comfortably in the running and Aug 20th was not.
That 14 day standard is not cast in stone. Ovulation can occur as early as cycle day 10 and occasionally earlier, which would put guy #1 in contention. As Annie says, an early ultrasound would help here. Without the ultrasound, the chances seem high for guy #2 being the winner.
Hi, Ashr, did you get the 5w6d count just from counting forward from your last period, or did you get it from an ultrasound?
If the websites are correct that you got pregnant on the 27th, it could not be the first guy. But they are only as good as the information that goes into them, and counting forward from the last period is not as precise as you need, to rule either guy in or out. An ultrasound in the next week would be able to confirm with a lot of certainty.
Unfortunately, if you wait too long for an ultrasound, it won't be precise enough to tell you what you need to know, because babies' growth rates can vary. But if you get it in your sixth or seventh week [counting from the first day of your last period] that should be precise enough. Don't wait longer than that, and if your doctor won't give you one, see if you can find a doctor who will.