I understand how to alter the bottom of the writer permalinks, however on my small site, I make reference to customers not by their username but with a number according to their User ID, so User number 5 authored this publish, instead of JohnDoe123 authored this publish.

The issue comes after i visit that customers archives and rather than seeing something similar to example.com/authors/5/ I see example.com/authors/johndoe123/ .

How do you change permalinks to ensure that I'm able to pull-up author archives while using following structure? :

[wordpress_site_url]/authors/[user_ID]/

You can do this with the addition of new rewrite rules for every user in much the same way you'd when altering or getting rid of the writer base. So, adapting code from the previous answer, you'd add your rewrite rules something similar to this:

add_filter('author_rewrite_rules', 'my_author_url_with_id_rewrite_rules');
function my_author_url_with_id_rewrite_rules($author_rewrite) {
  global $wpdb;
  $author_rewrite = array();
  $authors = $wpdb->get_results("SELECT ID, user_nicename AS nicename from {$wpdb->users}");    
  foreach ($authors as $author) {
    $author_rewrite["authors/{$author->ID}/page/?([0-9]+)/?$"] = 'index.php?author_name=' . $author->nicename . '&paged=$matches[1]';
    $author_rewrite["authors/{$author->ID}/?$"] = "index.php?author_name={$author->nicename}";
  }
  return $author_rewrite;
}

After which filter the writer link:

add_filter('author_link', 'my_author_url_with_id', 1000, 2);
function my_author_url_with_id($link, $author_id) {
  $link_base = trailingslashit(get_option('home'));
  $link = "authors/$author_id";
  return $link_base . $link;
}

Really I do not want to produce rules for every user within this situation, the next two rules should suffice:

add_filter('author_rewrite_rules', 'my_author_url_with_id_rewrite_rules');
function my_author_url_with_id_rewrite_rules($author_rewrite) {
  $author_rewrite = array();
  $author_rewrite["authors/([0-9]+)/page/?([0-9]+)/?$"] = 'index.php?author=$matches[1]&paged=$matches[2]';
  $author_rewrite["authors/([0-9]+)/?$"] = 'index.php?author=$matches[1]';
  return $author_rewrite;
}