[{"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({$and:[{"grades.score":{$gt:5}},{"grades.score":{$not:{$lte:5}}}]})