Things I am attempting to do is: I wish to show 5 posts within the sidebar, EXCLUDING all individuals publish I labeled "hewlett packard" (ID=11). Apparentely you will find lots of method of doing by using groups, however with tags it really is difficult to find.

This is actually the code I've.

<?php query_posts( array( 'tag' => -11, 'posts_per_page' => 5, 'orderby' => 'date', 'order' => 'DESC' ) ); ?>
<?php while (have_posts()) : the_post(); ?>
<?php if (class_exists('MultiPostThumbnails')
            && MultiPostThumbnails::has_post_thumbnail('post', '3-image')) :
                MultiPostThumbnails::the_post_thumbnail('post', '3-image'); endif; ?>
<div>in <?php   the_category(', '); ?></div>

<?php   the_title(); ?>
<?php
$count = 0;
$posttags = get_the_tags();
if ($posttags) {
foreach($posttags as $tag) {
$count++;
if ($count <= 1 ) {
echo '<a href="' . get_tag_link($tag->term_id) . '">' . $tag->name . '</a> ';
}
}
}
?>
  <?php endwhile;?>

It shows only 5 posts, showing just the first tag, however it keeps the posts using the tag I'm attempting to exclude.

I'm not a programmer, so I am certain you will find lots of other solutions with code i possibly could hack to have it right.

Any assistance will be appreciated.

You should utilize WP_Query class together with tag__not_in.

<?php
$the_query = new WP_Query( array( 'tag__not_in' => array( 11 ) ) );

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

     // Whatever you want to do goes here

endwhile;

// Reset Post Data
wp_reset_postdata();
?>

You will get more details about WP_Query class here - http://codex.wordpress.org/Class_Reference/WP_Query