Why doesn’t /2013/01/ properly return January’s archives in archive.php?

Don’t use query_posts in the template for simple modifications of the main query. Use the pre_get_posts action instead to modify the query before it runs:

function wpa_date_posts_per_page( $query ) {
    if ( !is_admin() && $query->is_date() && $query->is_main_query() ) {
        $query->set( 'posts_per_page', 5 );
    }
}
add_action( 'pre_get_posts', 'wpa_date_posts_per_page' );