Exclude posts of specific categories from blog homepage. Source: http://www.wpmayor.com/how-to-hide-or-remove-categories-from-a-wordpress-homepage/

exclude-posts-blog-homepage.php

<?php

//* Exclude categories from blog homepage
function customprefix_exclude_categories_home($query) {
    if ($query->is_main_query() && $query->is_home()) {
        $query->set('cat', '-5,-34'); // Precede category IDs with a minus sign
    }
}
add_action('pre_get_posts', 'customprefix_exclude_categories_home');