I am trying to make a custom loop that will display the latest 5 posts from select categories, all using a single query. I want the loop to display the category name followed by the 5 posts, and then the next category, etc.

I followed this answer and it seems to do what I want, except it doesn't output the categories properly.

For example, let's say I want to display categories 100,101,102 and 103, it should display like this:

100 Post 1 Post 2 Post 3 Post 4 Post 5

101 Post 1 Post 2 Post 3 Post 4 Post 5

etc.

However, currently, if there is a post in category 100, and also in category 250, it will also display the title of category 250 too, like so

250 Post 1

How do I get it that it ONLY displays the categories specified?

Here's the code I have so far, based on this.

<?php

$args = array(
    'posts_per_page' => -1,
    'tax_query' => array(
        array(
            // arguments for your query
            'taxonomy' => 'category',
            'field' =>  'id',
            'terms' => $selected_categories, // $selected_categories contains an array of post IDs.
        )
    )
);

$query = new WP_Query($args);   
$q = array();

while ( $query->have_posts() ) { 

    $query->the_post(); 

    $a = '<a href="'. get_permalink() .'">' . get_the_title() .'</a>';

    $categories = get_the_category();

    foreach ( $categories as $key=>$category ) {

        $b = '<a href="' . get_category_link( $category ) . '">' . $category->name . '</a>';    

    }

    $q[$b][] = $a; // Create an array with the category names and post titles
}

/* Restore original Post Data */
wp_reset_postdata();

foreach ($q as $key=>$values) {
    echo $key;

    echo '<ul>';
        foreach ($values as $value){
            echo '<li>' . $value . '</li>';
        }
    echo '</ul>';
}

?>

Thanks for any help!