[{"_id":1,"items":[{x:"one",y:"two",z:"three"},{x:"four",y:"five",z:"six"}]}]

db.collection.aggregate([{$match:{_id:1}},{$project:{item:{$first:{$filter:{input:"$items",cond:{$eq:["$$this.y","five"]}}}}}},{$project:{indexValue:"$item.z"}}])