Why can't I access my S5's test menu?
Because Verizon thinks you have no need to get into hidden menus. You'd have to explore other options which are unsanctioned.
Thanks it also appears that Verizon is getting worse with respect to customer service
I think VZW is fine for customer service.
Those hidden menus offer lots of options and some that can mess up your device. VZW makes it so that you don't actually mess it up and then demand a replacement after doing so.
What are you trying to do?
My compass app were not pointing to North so a developer suggested that I use the hidden menu to try to "zero in" my compass apps.