my iphone 5 randomly turns off by itself

my iphone 5 randomly turns off by itself but before it turns off a blue screen (the blue screen of death) shows up and then it turns off when i try to turn it back on the apple logo shows up and then that screen gets all black and white and pixilated but the apple logo is still on the screen sometimes the screen turns yellow and other colors i just got my iphone in july so it's pretty new the battery seem to be alright.... ive tried restarting the phone, recalibrating it, restoring it and nothing is working