Thanks for your query.
Technically, sperm survives for about 3 - 5 days, and the mature egg is viable for 24 hours after ovulation.
So there is always technically a chance for conception around the dates that you mention.
If you have conceived in january, you would miss your period that is due on the 4th of January, and if you have regular cycles, you can take your pregnancy
test anytime after the 5th of February.