My last menstral cycle started June 25. It lasted about 5 days. I had unprotected sex July 5 and again July 15. I took a test that told me I am 2-3 weeks pregnant. Which date was I most likely to conceive

There is no way for us to know when you conceived. Ovulation and conception differ from woman to woman. If paternity is in question you will need to have a DNA test done after the baby is born.