I’ve come up with a better way than in my previous answer:
First you need to set up an array containing the slugs of the tags you want to exclude. Then loop over that array, and on each term, use get_term_by()
to get the tag, saving its ID to another array. That is what you can pass through to your query.
$tag_slugs = array(
'foo',
'bar',
);
$tag_ids = array();
foreach( $tag_slugs as $slug ) {
$tag = get_term_by( 'slug', $slug, 'post_tag' );
$tag_ids[] = $tag->term_id;
}
$args = array (
'posts_per_page' => 5,
'paged' => $paged,
'post__not_in' => get_option( 'sticky_posts' ),
'tag__not_in' => $tag_ids,
);