After many searches through various forums on setting customized notifications for my contacts, and after many attempts at the given suggestions, all of which failed to work for individual customization (and I am not phone ignorant)I could select a notification tone different than the installed one but it only worked for all my contacts, not just the one I wanted it to alert me to. I finally went to the Verizon store. I was told that every batch of phones have glitches and that was my burden to bear. Thank you very much. I'm stubborn. Finally, after 8 months of trying every known suggestion this is what I found that does work - Galaxy S5, Verizon Carrier, Message+ user....
1. Go to a received message in your messaging app
2. Find the three dots by the phone symbol in the upper right corner
3. Click Customize - top of the list
4. Click Tones - 4th down the list
5. Select the app you want to select your tone from (if you have more than the one that came with the phone)
6. Select the tone
7. Click on "Set Notification" on the bottom left of your screen and you're good to go