To get the tax terms for that page you can use this:
https://codex.wordpress.org/Function_Reference/get_the_terms
Then plug this into a get_posts
get_posts(array(
'post_type' => 'quotes',
'tax_query' => array(
// get_the_terms() stuff.
),
'order' => 'ASC',
'posts_per_page' => 5,
'orderby' => 'rand')
);
?>
Note: This is off the top of my head but I hope it sets you on the path to your answer 🙂