Is this normal on an iphone?

We'll I just bough a used iphone 5 and it's kind of scratched up on the sides. We'll anyways about every 3 minutes it loses one percent of battery life and I did the math(although I'm not sure till just lose life every 3 mins) and it said that if it does loses life every 3 minutes it should give me at least 300 minutes of use when fully charged but I think the battery will die much faster later on… So is it normal for the battery to run out this quickly?

P.s. I turned off the unnecessary things like location services, Siri, Bluetooth, auto brightness, etc.
and if it's not normal please tell me how to fix this.
Whoever tells me what I need I will give you as much points as I can

It is not normal specially for an iPhone, unless it was an android(which I have). If you bought the phone used, chances are it has some battery problems. You should have apple look at it an replace it for a new one. All apple products are covered by a one year warranty that covers things like bad batteries. IPhone 5 one main defect when it came out was that they kept overheating therefore battery life wouldn't last, use THIS as an excuse to get them to replace it.