How to limit number of "Promoted to Front Page" option for each user/role
You can achieve above by writing a small custom module in Drupal... Steps are outlined below to achieve the same.


Create install file and define schema hook with table name as user_promote_counter with below fields
uid, timestamp, nid
Using hook_node_presave($node) update above table with a record of uid, timestamp, nid of the node updated whenever promote is set to true so that you can track only promoted to front page actions.
Use hook_node_validate($node, $form, &amp;$form_state) in your custom module to verify current user who has promoter role exceeded the limit of 5 by querying above table using timestamp and uid columns. Raise an error if limit is exceeded. That will prevent user to promote more than 5 nodes per day.