$categories = get_categories();
foreach($categories as $c) {
    echo \'<h2>\'. $c->name . \'</h2>\';
    $posts = get_posts(array( \'category\' => $c->term_id, \'numberposts\' => 5 ));
    foreach($posts as $post) {
        echo $post->post_title;
    }
    ?>
    <a href="<?php echo get_category_link($c->term_id);?>">
        View all posts in <?php echo $c->name;?>
    </a>
    <?php
}