Drupal 5.x version of: http://drupal.org/node/113696

Using the 4.x code from the link above I created a mini module and decided to name it 'moderation_skip'. Perhaps a more accurate name would be 'auto-publish' or something like that, but you get the idea.

1. Create a directory under modules named moderation_skip.

2. Put the following in moderation_skip.module:

<?php

/**
 * Implementation of hook_perm().
 */
function moderation_skip_perm() {
  return array('skip node moderation');
}

/**
 * Implementation of hook_nodeapi()
 *
 * Set the moderation state of a node
 */
function moderation_skip_nodeapi(&$node, $op, $teaser = NULL, $page = NULL) {
  switch ($op) {
    case 'submit':
      if ($node->status != 1 && user_access('skip node moderation')) {
         if (!user_access('administer nodes')) { // Don't reset for admins
            $node->status = 1; // Publish the node.
            $node->moderate = 0;
         }
      }
      break;
  }
}

?>

3. Put the following in moderation_skip.info:

name = Moderation skip
description = "Allow users with certain roles to bypass node moderation."
version = "5.x-0.1"

4. Visit modules admin page and enable the new module.

5. Visit role permissions and grant the 'skip node moderation' permission to any roles required.