iPhone 5 shuts down even when it's on the charger

My iPhone 5 keeps shutting down even when it has full battery. It doesn't last more than 2 minutes on and that's when I am able to turn it on. When I connect it to the charger sometimes it just flashes the apple continuously. I noticed that when it's on sometimes it doesn't connect to the Wi-Fi and I have no signal it just says searching. It just started doing all this 3 days ago, befire that it worked perfectly fine. Does anyone know what could be wrong with it?