PHP - Deletion of Registration above 10

Good, I would like information on Deletion of records greater than 10. This is ...

If the database has 10, the function does not work! If the database is above 10, delete X old records until you get 10 again.

I'm using it like this ...

   $stmt = $con->prepare("SELECT client_id FROM public_rewards WHERE client_id = ?");
   $stmt->bind_param('s', $_SESSION['u_id']);
   $stmt->execute();
   $stmt->bind_result($uid);
   $stmt->store_result();       

   if($stmt->num_rows > 5) {

        while($row = $stmt->fetch()) {          

            $remove_favorite = "DELETE FROM public_rewards WHERE client_id = '$uid' ORDER BY DESC";
        }           
   } else {
       return false;
   }   

I was a bit disoriented, because this function erases EVERYTHING! And I do not want it all .. just stick with recent 10.