There are only two ways to do it free. Neither is good. 1) Use a free autoresponder service. They will put ads in your messages, and you won't have full control/reports like you would with a paid version. 2) Host a autoresponder script on your own. One or two spam complaints will have your domain blacklisted and nobody will be reading your messages after that ('cause they aren't getting them).
Or a PHP code to send the newsletter in HTML format (nicer) and even a MyQSL DB for the email addresses (or even a TXT file) Am I wrong?
I've used streamsend.com They seem pretty legit. I pay $50/month to send up to 50,000 mails. So I imagine the rate is quite lower for 5000/month.
Don't forget about Swiftpage - If you keep your list in Outlook or Excel we have an integrated solution that sends directly from the application.