Can you conceive with protection?

Im truly confused about if I am pregnant, My menstrual went off day before Christmas day. Early morning on 26th I had intercourse with protection. It was stated from my partner that it was tight. Question is it possible to conceive with protection as well when did I ovulate if the sperm did leak? It said on the ovulation calendar the 30th , but when put in pregnancy calendars it said based on last menstrual date the 3rd of January , their is no way possible the sperm days in 5 days. Their s no way the sperm can survive from the 26th to 3rd , When they conceiving dont they mean right on that date ?