Samsung Galaxy S5 died suddenly and without reason Less than a month old my Samsung Galaxy S5 has completely died.

I was listening to music on my Galaxy S5 (&lt;1 month old) when it cut out. The phone had 50% charge, but had suddenly turned itself off. 

I restarted it and it showed only 10% battery life, so I turned it off--thinking this might be a battery calibration issue and I'd charge it when I got home and all would be dandy.

I charged it to 100% once home and began using it, and suddenly, the battery life began dropping 99, 97, 96, 95 probably once every second (the phone was also very hot) it died completely and will not turn on, will not charge, will not show any signs up life. Zero.

I've taken it out of the Otterbox case, taken out the battery, removed the SIM and micro SD card and still zero signs of life. Any idea what could have caused this of how to fix it?
This is likely a defective battery or similar. Seeing as you have just bought it, I'm not surprised that it is showing this behavior. You could probably pull up your warranty (assuming you haven't rooted it) and get it fixed for no charge.

In case it is not a defective battery, hold down the power button in addition to holding both volume button for about 10 seconds or so. If that doesn't turn it on I'd treat it as defective and get it fixed/replace the battery yourself (probably voids warranty, be careful)