database.json

{
  "rules": {
    ".read": "auth != null",
    "users": {
      "$userId": {
      		".write": "$userId === auth.uid"
    	}
    }
  }
}

storage.txt

function isCorrectUser(userId) {
	return request.auth.uid == userId;
}

function isLessThanNMegabytes(n) {
	return request.resource.size < n * 1024 * 1024;
}

service firebase.storage {
  match /b/{bucket}/o {
  	allow read;
    match /user-images/{userId}/{allPaths=**} {
    	allow write: if isCorrectUser(userId) &&
      								isLessThanNMegabytes(5);
    }
  }
}