WordPress already generates class for each posts, you can use these classes using the post_class
function.
Note: The function can be used either within the loop or by passing the $post_id
So you would have
<ul>
<?php $the_query = new WP_Query( 'posts_per_page=5' ); ?>
<?php while ($the_query -> have_posts()) : $the_query -> the_post(); ?>
<div id="post-<?php the_ID(); ?>" <?php post_class( 'post' ); ?>>
<a href="https://wordpress.stackexchange.com/questions/250637/<?php the_permalink() ?>"><?php the_title(); ?></a>
<?php the_excerpt(__('(moreā¦)')); ?>
</div>
<?php
endwhile;
wp_reset_postdata();
?>
</ul>