If there are five boys and no girls born into a family does that increase the likelihood that the sixth offspring will be a girl?

No, the likelihood of the sixth offspring being a girl is not influenced by the previous births. In humans, the sex of a child is determined by genetics, specifically the combination of sex chromosomes from the parents, and each birth is an independent event. Therefore, the probability remains approximately 50% for a girl and 50% for a boy, regardless of the sexes of the previous children.