How to sort random posts by date?

Is it possible to display random posts within 30 and omit duplicate post?

<ul><li><h2>Random Posts</h2>
    <ul>
 <?php
 $rand_posts = get_posts('numberposts=5&orderby=rand');
 foreach( $rand_posts as $post ) :
 ?>
    <li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
 <?php endforeach; ?>
    </ul>
 </li></ul>

Thank