On a new Galaxy S5, the wifi hotspot state can only be toggled via Settings. I have so far found no other application (e.g. widget, or NFC app) that can successfully toggle it. A brief "checking subscription status" message appears on the screen, and then nothing happens (or, depending on the app, an error is reported).
My educated guess (I'm a software developer myself) is that Verizon's software that extends Android to validate the subscription is misbehaving. Everything works fine from Settings; I have an Unlimited plan and tethering works as it should.
I reported this problem to Samsung, but their answer was basically "it works". (But it doesn't.) There are a fair number of similar reports on Android-related Web sites, some involving the S5, some the Razr Maxx.
It would be really, really nice if this could get fixed or if there's a workaround. I'm particularly vexed by the inability of NFC apps to toggle this state.