Randomly show one item from the last x posted
Sort your View by Content: Post date (desc) and set the Pager to Use pager: Display a specified number of items | 5 items



Go to the Advanced Settings in the view and click in the Theme: Information



Search the Style output: section and select a name, in my case was views-view-unformatted--temp.tpl.php

Go to the folder YOUR_SITE/sites/all/modules/views/theme and copy to your theme folder the file views-view-unformatted.tpl.php and rename it to views-view-unformatted--temp.tpl.php

Edit your new file views-view-unformatted--temp.tpl.php and put inside only this code to show only one element:

&lt;?php

/**
 * @file
 * Default simple view template to display a list of rows.
 *
 * @ingroup views_templates
 */
 //Selecting one element from your last 5 posted elements
 $element = $rows[rand(0, 4)];
 $rows = array();
 $rows[] = $element;

?&gt;
&lt;?php if (!empty($title)): ?&gt;
  &lt;h3&gt;&lt;?php print $title; ?&gt;&lt;/h3&gt;
&lt;?php endif; ?&gt;
&lt;?php foreach ($rows as $id =&gt; $row): ?&gt;
  &lt;div&lt;?php if ($classes_array[$id]) { print ' class="' . $classes_array[$id] .'"';  } ?&gt;&gt;
    &lt;?php print $row; ?&gt;
  &lt;/div&gt;
&lt;?php endforeach; ?&gt;


In the View go to the bottom of the Information window and click Rescan template files and click OK, then save your View.



And go to see your result.

Attention: Remember to repeat these steps if you ever change theme.