Lazaros,
I'm not sure if this will help, but I had the same problem a couple months ago. I couldn't see the S5 Theme Options in the backend of Wordpress.
So I took Dominic's advice and I updated:
1. Vertex to latest version;
2. My template to the latest version;
3. Then php from v5.6.31 to v7.3.
Now I can see the Theme Options under Appearance in the backend. Hope this helps in some way.
Jeff