Add class every 4 post like , class_1, class_2, class_3, class_4 and class_1, class_2, class_3, class_4

You can try something like this:

if ( have_posts() ) : 
    
    // define count var ##
    $count = 1; 

    while ( have_posts() ) : 

        the_post();

?>
        <div class="class_bg_<?php echo $count; ?>">XXX</div>
<?php

    // iterate ##
    $count ++;

    // reset count if reached 5 ##
    if( 5 == $count ){ $count = 1; }

    endwhile;

endif;