Alternatively, you can utilize the following code snippet:
$('#multimenu a').hover(function(){
$(this).next().show();
},function(){
$(this).next().hide();
});
To see it in action, check out the demo here:
http://jsfiddle.net/s6EXf/5/
Make sure to update your HTML structure as follows:
<ul id="multimenu">
<li><a href="#">Example 1</a><div class="submenu"></div></li>
<li><a href="#">Example 2</a><div class="submenu"></div></li>
<li><a href="#">Example 3</a><div class="submenu"></div></li>
<li><a href="#">Example 4</a><div class="submenu"></div></li>
<li><a href="#">Example 5</a><div class="submenu"></div></li>
</ul>
Furthermore, by using CSS pseudo class :first-child
, you can eliminate the need for the first child class.