all from all categories except for one where I want only 5..

I’m working on a site where its all based on categories, all posts are shown on index and are filtered with jquery. Works wonders! Just that one category are normal blogposts and I dont want the content to drown in blogposts.

So my question is:
Is there a way to show only 5 blogposts from the category ‘blogg’ and all the posts from the other categories? And then when filtering on ‘blogg’ see all blogg-posts, not just 5?

The code I have for now is:

$args = array( 'numberposts' => -1, 'orderby' => 'rand');

		$rand_posts = get_posts( $args );
		foreach ( $rand_posts as $thumbnail ) {
      		if ( has_post_thumbnail( $thumbnail->ID ) ) {
              $categories = get_the_category( $thumbnail->ID );
              $cat_slug = "";
              if ( $categories ) {
              	$cat_slug = $categories[0]->slug;
              }

			$large_image_url = wp_get_attachment_image_src( get_post_thumbnail_id($thumbnail->ID), 'thumbnail');
			$placeholder = get_bloginfo('stylesheet_directory')."/assets/placeholder.gif";
			$thumb = get_the_post_thumbnail( $thumbnail->ID, 'thumbnail' ); 

			echo '<a class="showdiv"  href="' . get_permalink( $thumbnail->ID ) . '" title="'.esc_attr( $thumbnail->post_title ).'">';
            echo ' <div class="'. $cat_slug. ' element">';
            // echo get_the_post_thumbnail( $thumbnail->ID, 'thumbnail' );
			echo "<img class='lazy' data-original='$large_image_url[0]' src='$placeholder'>";
            echo "</div>";
           	echo "</a>";
        }
}

And the menu with filtering:

<?php
	$args=array(
	  'orderby' => 'term_group',
	  'order' => 'DESC'
	  );
	$categories=get_categories($args);
	echo '<ul id="filters">';
	echo '
<li> <a href="'.home_url().'" title="Allt">Visa allt</a> </li>
 ';
	  foreach($categories as $category) {
	    echo '
<li> <a href="'.home_url().'">name.'" data-filter="' . $category->slug. '">' . $category->name.'</a> </li>
 ';
	    }
	echo '';
	?>

Very very grateful for any suggestion!