Even if you have a clean list, that number of emails, especially if they are going to just a few ISPs, will get your server rate limited or blacklisted. In general, I recommend that email be split along these lines:
Transactional Emails
These are shipping notifications, password resets, forum notices etc. Basically computer to user type emails where a reply is not expected.
Marketing/Newsletters
Mailings to any list even if they are not specifically marketing related. For example, if you ran a forum with 100K users, I would not recommend blasting these emails from your forum server it it sends the transactional emails.
Business Purposes
Business/personal correspondence.
Ideally, you want to use different IPs or delivery methods for each class of email. However, I often find that budget or other issues does not permit this preferred setup.
In these cases, evaluate the impact of combining any two channels.
In your case, I would not let a customer regularly send to 5000 subscribers through a shared hosting system. If the server is dedicated, if they send transactional emails through there, then I would advise them not to do so or risk getting blacklisted.
I would recommend they use a email service provider -- especially if this is on a shared host.
Plesk 11+ & Postfix
Note that on Plesk 11+ on Postfix, sites with a dedicated IP addresses send email from that IP. This may be a workaround for you to limit the damage if you must use your server for bulk emailing.
This is getting a bit dated, but if you do get blacklisted:
http://www.rackaid.com/blog/spam-blacklist-removal/