Thanks so much for your help. I am almost there, it is kind of working.
I am using
<?php
foreach((get_the_category()) as $category) {
$posts = get_posts("category=" . $category->cat_ID . "&numberposts=5&offset=5");
if( $posts ) :
?>
<div class="recent-posts">
<h2>Most Recent in <?=$category->cat_name?></h2>
<ul>
<?php foreach( $posts as $post ) : setup_postdata( $post ); ?>
<a href="<?php the_permalink() ?>" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></li><br />
<?php endforeach; ?><br />
</ul>
</div>
<?php endif; ?>
<?php } ?>
I have it in the sidebar, but I am not sure that is going to be right.
I want it to show up when a reader looks at
a/ the main page (so it shows the titles of post 6 though 10)
b/ a category listing, aslo showing post 6-10 for that category
but it is getting stuck in showing only the things for the last category selected on both the page and in the side bar.
Any suggestions?