Display 5 recent posts in single.php?

for details, review:
https://codex.wordpress.org/Template_Tags/get_posts#Examples

modified code (untested):

<ul>
<?php
$this_post = $post->ID;
$latest = get_posts( array( 'posts_per_page' => 5, 'post__not_in' => array( $this_post ) ) );
foreach( $latest as $post ): setup_postdata( $post );
?>
<li><?php the_time(get_option('date_format')); ?> | <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach;
wp_reset_postdata(); ?>
</ul>

get_posts() https://codex.wordpress.org/Template_Tags/get_posts uses the same parameters as WP_Query() https://codex.wordpress.org/Class_Reference/WP_Query#Post_.26_Page_Parameters

the content of each post to show up below the title.

the ‘below’ might need some CSS and possibly some html tags with CSS classes.

I want for the FULL post to appear.

are you using the ‘more tag’ in your posts?

this might apply to your case
https://codex.wordpress.org/Customizing_the_Read_More#How_to_use_Read_More_in_Pages

I posted the wrong link, should be
https://codex.wordpress.org/Customizing_the_Read_More#More_about_.24moreinstead of just:

<?php the_content(); ?>

have you tried this:

<?php
global $more;
$more = -1;
the_content(); ?>

But is it ok to display multiple posts in the single.php? Do you think it will mess up something else?

any mess is unlikely, when you are using wp_reset_postdata() in the code.