I bought a Nexus 5 a year ago and it has been running fine. After the Lollipop update, my phone has started crashing. Even though the phone has enough battery, if I run any app for like 5 minutes (it happens for any app, no particular app I could isolate), the phone just crashes to a black screen. When I start it again, the battery has suddenly gone to zero from its initial healthy number (e.g. 40%) and the phone shuts down again (sometimes even at the loading stage after the "Google" display on starting). But if I charge my phone even for a second after it crashes and then restart it, then the battery shows up as 40% (or whatever it was pre-crash) again. But then the phone crashes again after I use it. If I don't run any apps, then the phone does not crash.
Does anyone know the solution to this problem? Please help because now I can't use my phone even for 5 minutes without giving it a charger jumpstart!
Note: The phone never crashes when it is plugged to a charger no matter how many apps I use. It only crashes if it's unplugged.