First, 30% is FAR loo low to drag a battery down to. You should charge it at 50%. Allowing it to run down to 40% won't shorten the life that much. After that, it can. (It might also lead to dendrites - which mean a new battery - but the jury is still out on that one. And it's a HUGE jury - the automotive industry.)
Second, an unexpected drop from 30% to 5% is almost always a small dendrite (which, again, means replacing the battery).
What it sounds like is that the phone ran down past the precharge point - which means that the phone's internal charging circuitry can't charge it. Since the battery can't be removed (there are external chargers that can revive almost "not there any more" batteries), it has to go to a repair shop.
In the future - for anything using a lithium battery (lithium batteries are not deep-discharge batteries), start planning on recharging it as it drops to 50%. By the time you get to recharge it, it should be between 40% and 50% - which will keep it going for a long time.