Is it possible to have sex the 1 or 2 days before your period started, and conceive 5-7 days later, from that intercourse-the day before your menstruation started? The menstruation had ended, so the sperm would have had to survive the menstrual period. Is that possible?

It's not the norm, but yes, it is possible. If a woman tends to ovulate early, or just happens to as a one off in any given cycle, her body could be shedding the lining designed to support the pregnancy that didn't take place, while preparing for the next ovulation with a change in the environment to support sperm for a few days.

It doesn't usually happen due to hormones that are required at levels to produce these changes being different during your period.

Just prior to ovulation sperm may live several days... although most only for a few days. Other times of the cycle they die off quickly.

If you wanted to pick the least likely, although not impossible, time to get pregnant in a cycle, sex just before a period would be it. Always wise to use birth control to make the possibility even less likely regardless of where you are in your cycle.