Whether a woman can get pregnant from a little sperm, perhaps less than half of the drop, which somehow gets into the vagina, five days before period?

Conception. If a woman has regular 28 day cycles, she is most likely to get pregnant 14 days prior to her period, or after for that matter. 5 days before the period is usually a less fertile time, but of course anything is possible. Less fertile is not infertile.