Show 1 random node out of the 5 most recent in views
I wasn't able to get this working within views proper, so I added a subquery instead.
There are three relevant things that need to be set up in your initial view to get this to work:

Filter Criteria: Content: Type = 'my content type' (blog post in
the attached image)
Sort Criteria: Global: Random
Pager: Use Pager: Display a specified number of items: 1


As it is, that will get you a view that will pull in 1 random result from among all content of type &quot;my content type&quot;.
But the question is asking you to pull in 1 item from the last 5 created posts, not from all posts.
To do that, you need to add an additional where condition. That can be accomplished with this snippet:
/**
 * Implements hook_views_query_alter().
 *
 * Limits results to the most 3 recent blog posts.
 */
function MY_MODULE_views_query_alter(&amp;$view, &amp;$query) {
  if ($view-&gt;name == 'MY_VIEW_NAME' &amp;&amp; $view-&gt;current_display == 'MY_CURRENT_DISPLAY') {
    $query-&gt;add_where_expression('AND', &quot;node.created &gt; (SELECT node.created AS created
      FROM
      node node
      WHERE  (type = 'MY_CONTENT_TYPE')
      ORDER BY created DESC
      LIMIT 1 OFFSET 5)&quot;);
  }
}

That snippet says:
&quot;Find me the creation timestamp of the node that is the fifth-newest. Then filter my final result by nodes with creation timestamps greater than that.&quot;
There might be a better way, but this works for me.