OK so I had unprotected sex on November 5th and then had a period that started on November 11th and ended on November 20th and now its December 20th and I had a positive home pregnancy test is it possible that I conceived on November 5th

It is possible that you conceived on the 5th November and highly likely and the period you experienced could have been implantation bleeding. Did you have unprotected sex again after this date? If so and you are unsure of the dates explain this to your doctor. If you did not have unprotected sex since it is highly likely that this was when you conceived although no protection is 100%