Allison Jon, the manager of an $800-$number reservation service for a nationwide chain of luxury hotels, is concerned about the productivity of her operation. Analysis of past data shows that it should take an average of five minutes to properly process a reservation. To setup a control chart for reservation service time, Allison records the time it takes to complete the reservation. She randomly samples $5$ reservations every day for $30$ days.

$1.$ What is the lower control limit for the X$-$bar chart? Enter your response to $3$ decimal places.