I had done this. But it only blocks the phone call. Not the text.
I'm assuming the same as one of the other guys here. I bet if I called Verizon they offer it as a fee. Which is a load of BS.
And yes, it is an S5.
Originally Posted by jetskier
On my AT&T model using AT&T messages, you click the message, then menu (3 vert. dots). Then add click "add to contact"..."create new". then name it and save it. Within that same new contact, click the menu button at top right. There is an option to "add to reject list".
it may be similar on Verizon if it's not in the top level menu.
You basically just need to add this to your CSC settings and it will enable a dedicated call/message blocking options in your settings.
This was posted for the Note 1 at the time but I tried it on my Note 3 and it works perfectly fine. I'm thinking it will work perfectly fine for your S5's.
Here's the original thread with full instructions how-to! All credit goes to Majdinj :
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