[{"name":"Doc One","grades":[{"grade":"A","score":1},{"grade":"A","score":12},{"grade":"A","score":7}],"borough":"Manhattan2"},{"name":"Doc Two","grades":[{"grade":"D","score":6},{"grade":"D","score":7},{"grade":"F","score":8}],"borough":"Brooklyn"},{"name":"Doc Three","borough":"Queens"},{"name":"Doc Four","grades":[],"borough":"Bronx"}]

db.collection.find({"grades":{"$not":{"$elemMatch":{"score":{"$lte":5}}}}})