Change content off every sixth element

query_posts should only be used for the main loop. Instead, use a new instance of the WP_Query class:

$my_query = new WP_Query( array( 
    'post_type' => 'post', 
    'posts_per_page' => 10, 
    'order' => 'DESC', 
    'paged'=> $paged
) );

echo '<ul>';

while ( $my_query->have_posts() ) : $my_query->the_post();

    if ( $my_query->current_post > 0 && ( $my_query->current_post + 1 ) % 6 == 0 ) {
        echo "<li>I'm odd one</li>";
    } else {
        echo "<li>" . get_the_title() . "</li>";
    }

endwhile;

echo '</ul>';

The above will “do the special thing” every sixth element. Should you just want it on the sixth itself, use $my_query->current_post == 5 instead (index starts at 0).