Usually when you ask someone "Do you have any brothers or sisters?" they will mention their "rank" in their reply. They will say "I've got two younger sisters" or "I'm the middle child, I've got an older brother and a younger sister." If they are not that specific in their response, then you can ask "Are you the oldest?" or "Are you the baby* in the family?"
*In AmE, the youngest child in the family is referred to as "the baby" by family members even when he or she is all grown up and has children and grandchildren of their own.