Normally you'll ovulate between days 11 to 16 of your cycle so from about November 2 to 7.
Sperm can survive about 5 days.
Having sex on the 27 sperm would be viable until about November 1.
Having sex on the 28 or later would be about when you'd ovulate. No one, not even your doctor, can tell you exactly when you ovulated OR when conception occurred.
You will need a DNA test to determine paternity. There is NO way around it.