Is very easy to update a drupal website. Since you follow the best practices of drupal development "Don't change the core code", ever use the override methods...

by example, to update of drupal 5.15 to 5.16.

cd /var/www/example.com/public_html
wget http://ftp.drupal.org/files/projects/drupal-5.16.tar.gz
tar -xzvf drupal-5.16.tar.gz --strip-component=1 --exclude=settings.php

obs.: some linux use --strip-path instead --strip-component

remember to backup your database before. :)

KISS.