Get TOP x Tags from selected posts

With an array containing the post IDs its easy

$post_ids = array( 167, 774, 787, 358 );
$tag_all  = array();

foreach ( $post_ids as $post_id ) {
    $tags = wp_get_post_tags( $post_id, array() );
    foreach ( $tags as $tag )
        array_push( $tag_all, $tag->name );
}

$result = array_count_values($tag_all);
arsort( $result );
$result = array_slice( $result, 0, 5 );

echo '<ol>';
foreach ( $result as $tag => $count ) {
    printf( '<li>%s (%d)</li>', $tag, $count );
}
echo '</ol>';

Walk over the post IDs, get the tags of each post. Add the tags to a result array ($tag_all). Then counting the values (array_count_values()), this gives you an array with key => value (key = tag, value= count). Now just sorting the result array (arsort()) and get the first 5 elements (array_slice()).
Create a nice outpout and finish.