Include link category as class

I’m trying display my links list like this, with the link category as a class:

<ul>
<li class="cat1"><a href="example1.com">Link 1</a></li>
<li class="cat2"><a href="example2.com">Link 2</a></li>
<li class="cat2"><a href="example3.com">Link 3</a></li>
<li class="cat4"><a href="example4.com">Link 4</a></li>
<li class="cat3"><a href="example5.com">Link 5</a></li>
<ul>

Is there any way to do this? This would get me close, but I have no idea how to add the category to the class:

<?php get_links('-1', '<li class=>', '</li>', '', FALSE, '_id', FALSE,
FALSE, 5, FALSE); ?>