Error 404 blog/page/2/

I guess you don’t need to target a taxonomy. You can use the code below:

function query_change_function( $query ) {
     $query->set( 'posts_per_page', 5 );
}
add_action('pre_get_posts', 'query_change_function');

You should wrap the $query->set( 'posts_per_page', 5 ); around with if ( ! is_admin() && is_home() ) {//the $query->set code}
to avoid it changing to 5-posts everywhere.