Post recent news with date and month styled on a page

Check out
https://templatic.com/demos/hospitality/

On the bottom left, there is a list of posts, with a date and month. I know how to style it. I just do not know how to echo out the post with the date and month.

<ul><?php wp_get_archives('type=postbypost&limit=5'); ?></ul>

This currently works.. and it will show this.

<li><a href='#' title='Example Post 5'>Example Post 5</a></li>

Am I using the wrong code in general? How do I add to that php code to make it look like this

<li><span>3 <small>June</s> </small> </span><a href='#' title='Example Post 5'>Example Post 5</a></li>

With the correct date tied to the post title?

Thanks in advanced
-O