Wordpress scheduled task is called but not executed

I created a plugin with a cron to update all posts of a certain type every 5 minutes. I installed WP Crontrol to check if the cron is registered correctly and everything seems to be okay.

This is how I registered my cron:

function custom_cron_interval( $schedules ) {
    $schedules['fiveminutes'] = array(
        'interval' = 300,
        'display' = __('Every five minutes')
    );
    return $schedules;
}
add_filter( 'cron_schedules', 'custom_cron_interval' ); 

if ( ! wp_next_scheduled( 'recalculate_all_scores' ) ) {
    wp_schedule_event(time(), 'fiveminutes', 'recalculate_all_scores');
}

It is registered correctly but when the function executes, nothing happens. For testing purposes I hooked the function to the save_post action. Everything works fine this way. But when the scheduled task is called, it won't execute.

Here is the code of the function

function recalculate_all_scores() {
    global $wpdb; 

    $customers = $wpdb-get_results("SELECT * FROM wp_posts 
                                WHERE post_type = 'customer' 
                                AND post_status = 'publish';");

    foreach ($customers as $customer){
        set_score($customer);
    }
}

function set_score($customer){
    $acf_key = "score";
    $score = rand(0,50);
    update_field( $acf_key, $score, $customer-ID );
}

I also added the following lines to my wp-config.php:

define('ALTERNATE_WP_CRON', true);
define('DISABLE_WP_CRON', false);

Any idea what is stopping the function from executing?

EDIT

• I'm aware that the wp_cron system is not a real cron and that it relies on site visits.
• If I execute the function manually it takes about 15 seconds so the PHP execution time limit should not be a problem.