2 day old iphone 5s turns off at 95% battery life and will not turn back on. HELP

Question

So I had an iphone 4s for two years, the battery started to not last as long, so with my upgrade I got the iphone 5s (greatttt). Anyways I had it for a month then all of a sudden I wasn't getting calls, it took over a minute for me to even get a call to send, then once I was on the call others couldn't hear me well, then it would drop (no problems with service, always happened with full bars).  Brought it to Apple store, they told me it was a combination between the phone and my SIM card.  They gave me a new one and recommended I go to verizon to get a new SIM card.  That same day literally 3 hours later, the phone turned off randomly at 65% battery and WOULD NOT turn back on.  I had to go back to the apple store, they restored my phone and almost gave me another new one. However they tested the battery and everything and came to the conclusion it was okay and that I needed to restore the phone and set it up as if I did not already have an iphone (not use icloud to bring EVERYTHING over) So we did that and it started to work, that was two days ago.  Over the course of the last two days I have SLOWLY downloaded my previous APPS, however the only way to download those are to do it from the "cloud" because apparently I can't just get them from the app store.  Well yesterday I got the blue screen of death, however it came back, I thought nothing except that it was over worked.  Tonight it went down to 1%, I left it on the charger until it was at 96%.  I had NO APPS open. Went to my calendar and added a event for tomorrow, put my phone down and then ten minutes later looked at it and its turned off.  It will not turn on, I tried rebooting pressing both buttons, Ive plugged it back it, switched outlets, switched cords, NOTHING.
Of course I wish I never got the iphone 5s at this point.
What now?
Back to Apple again?

Answer 1

Yep.
Just like cars, you lucked on a lemon.