Puedes usar la HOUR función para agregar una condición adicional en las horas:
select count(*) as total from tradingaccounts accounts
inner join tradingaccounts_audit audit on audit.parent_id = accounts.id
where date(audit.date_created) between date('2013-11-01 00:00:00') AND date('2013-11-01 23:59:59')
AND HOUR (audit.date_created) BETWEEN 5 AND 15
