Does anyone know how I can send about 5,000 eMail on a daily basis for free?
If you're sending mass emails, you have to watch out for the spam police. Most decent services don't offer a free option for more than a few hundred people on an email list, but you would want to get an account with a service like Aweber. It's definitely worth it, especially if you are a marketer of some kind or it is for your business.
If you are not a spammer, and (logically) you already have permission from those 5000 people to send them emails on daily basis, the easiest solution is to set up a free mailing list or groups (something like google groups or yahoo groups), make it moderated, then ask those people to sign up.
I've done this with groups of ++1,000 successfully.
Becky, for that amount of emails you should consider your paid options though. One reason most people pay for services is because your isp and the host for your domain might have issues with the amount of emails you are talking about. They might consider it spam. There are also Can-Spam regulations one needs to follow not to get blacklisted:
Paid services handle those issues themselves.
Just my two cents...
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