Listing a single category of posts in archive drop-down

I’ve split my posts into two categories, and I want to have separate archives for each category. I’ve managed to output a list of the most recent posts in each category using the following code (I just re-use the code and change the cat ID):

<?php _e('Recent News Entries'); ?>
<?php $recent = new WP_Query("cat=1&showposts=5"); while($recent->have_posts()) : $recent->the_post();?>
<a href="<?php the_permalink() ?>" rel="bookmark">
<?php the_title(); ?><?php endwhile; ?>

… however I haven’t been able to figure out a way to output a single category’s posts into a drop-down format. Any ideas?

Thanks
Mike