Your ISP will have a SMTP server but with a send of 5000 in a short space of time they are likely to block most of them.
The next option would be to setup one on your local machine.
Another option is to get a VPS as this is cheaper than a fully dedicated server and install a SMTP server if one isn't already installed, check with the provider to see if they allow bulk sending of emails - a lot don't.
The easiest way is to use a mail list service.
http://mailchimp.com/ is a very basic one.
Hope it helps
PS Don't be a spammer, ensure your list is opt in confirmed!