query_posts: Display a random post from the most recent 5 out of 10 posts?

I think this will do what you want:

$args = array(
   'cat' => 55,          // Your category id here
   'posts_per_page' => 5,
   'orderby' => 'rand',
   'ignore_sticky_posts' => 1
);
query_posts($args);
if (have_posts()) : while (have_posts()) : the_post();
      // Your code to display the post here
      break;  // Exit loop after first post
   endwhile;
endif;