sort post type posts and custom database table by date

I have a post type and a table in the database that I display with the following code. The code works well!

But I want this list sorted by date.

My database table:

|id             |
|message_author |
|message_date   |
|message_update |
|message_title  |
|message_status |
|message_content|

<?php
global $wpdb;
$user_id = get_current_user_id();
$message_table = $wpdb->prefix . 'messages_hb';
$messages = $wpdb->get_results("SELECT * FROM  {$message_table}  WHERE message_author =  $user_id AND message_status = 'reply' ORDER BY message_update DESC ");
$notices_query = array('post_type' => 'notice', 'numberposts' => 5);
$notices = get_posts($notices_query);
$output1 = array();
$output2 = array();
if ($notices) {
    foreach ($notices as $notice) {
        $output1[] = '<li><a href="">' . $notice->post_title . '</a></li>';
    }
}
if ($messages) {
    foreach ($messages as $message) {
        $output2[] = '<li><a href="">' . $message->message_title . '</a></li>';
    }
}
$output = array_map(null, $output1, $output2);
foreach ($output as $items) {
    $items = array_filter($items);
    foreach ($items as $item) {
        echo $item;
    }
}
?>