Exclude categories from blog homepage with the Genesis Framework.

functions.php

<?php
//* Do NOT include the opening php tag

//* Exclude categories from blog homepage
add_action( 'pre_get_posts', 'bg_exclude_categories' );
function bg_exclude_categories( $query ) {

	if( $query->is_main_query() && $query->is_home() ) {
		$query->set( 'cat', '-5,-7' );
	}

}