Create a hierarchical loop at predefined markup requirements

I was able to figure it out myself, here is the code:

    <div id="fullpage">

   <?php
//for each category, show 5 posts
$cat_args=array(
  'orderby' => 'name',
  'order' => 'desc'
   );
$categories=get_categories($cat_args);
  foreach($categories as $category) { 
    $args=array(
      'showposts' => 5,
      'category__in' => array($category->term_id),
    );
    $posts=get_posts($args);
      if ($posts) {
        echo '<section class="vertical-scrolling" data-anchor="' . $category->name.'">';
        foreach($posts as $post) {
          setup_postdata($post); ?>
          <div <?php if(has_term( 'slide', 'fp_type' )): ?>class="horizontal-scrolling"<?php endif;  ?>data-anchor="<?php the_title(); ?>">
          <article id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
                 // Here comes the content //
                </article>
                </div>
          <?php
        } // endforeach;
        echo '</section>';
      } // endif;
    } // endforeach;
?>

    </div>

It seems to work quite fine.

@Michael´s answer helped me a lot