I've outgrown my current home-grown email system and my webhost has informed me I'm very close to their email sending capacity limit, so I'm in need of a new solution to disseminate all my emails to my subscribers.

My email goes out once per day and is AUTOMATICALLY generated. Currently there are about 5k subscribers

I'm needing a service that can receive an email from my system and disseminate that email to all my subscribers automatically, without any intervention from anyone.

I'm not looking for an anonymous remailer. Everything is above-board here and the service solution I'm seeking will also need to be opt-in.

Does anyone know if such a solution exists?