Very very slow query. How can I improve it?

the following query is used in my WordPress blog, it gets the categories that a user has posted in. When he has a post in the category, the name of the category is shown.

It is a very very slow query because it is a big database and I have problems with the hosting company.

I have 3 categories, with id 3 called News, 4 called Articles and 5 called Others. My code is:

<?php
$author = get_query_var('author');
$categories = $wpdb->get_results("
    SELECT DISTINCT(terms.term_id) as ID, terms.name, terms.slug, tax.description
    FROM $wpdb->posts as posts
    LEFT JOIN $wpdb->term_relationships as relationships ON posts.ID = relationships.object_ID
    LEFT JOIN $wpdb->term_taxonomy as tax ON relationships.term_taxonomy_id = tax.term_taxonomy_id
    LEFT JOIN $wpdb->terms as terms ON tax.term_id = terms.term_id
    WHERE 1=1 AND (
        posts.post_status = 'publish' AND
        posts.post_author = '{$post->post_author}' AND
        tax.taxonomy = 'category' )
    ORDER BY terms.term_id ASC
");
?>

<ul>
    <?php foreach($categories as $category) : ?>
<?php if ( ($category->ID == '3')   || ($category->ID == '4')  || ($category->ID == '5')) { ?>
    <li>
        <a href="<?php echo get_category_link( $category->ID ); ?>/?author_name=<?php echo $curuser->user_login; ?>" title="<?php echo $category->name ?>">
            <?php echo $category->name; ?>
        </a>
    </li>
<?php } ?>
    <?php endforeach; ?>
</ul>

Thank you all!