Can you please help me find a mailing list that is free to use?

What is the size of your mailing list?

If you're doing anything of value, you don't need to worry about the "free" part, because you will be able to make money from your work, and this will enable you to pay for the services you need.  If you're not making money from your work, then the "free" part matters.  In that case you might want to approach the popular mailing list companies (SurveyMonkey, MailChimp, ConstantContact, etc) and ask them to donate their services in exchange for a share of your future revenues.  If they see value in your enterprise they may want to become a part of it.  Best of luck!

I have a Facebook page of nearly 100K followers.     I am guessing I will have 1-5K subscribers on my mailing list.

Why not just post to your social media accounts?  They are mostly, if not completely, free.  Email is kind of 20th century.

Because the bulk of our members are old fashioned and prefer email.   Its something where we just want to have the option to do it, and would like to do a newsletter piece as well.

I used Cooler Email which is very neat and simple. It is not free but worth spending little money to use larger way.