Do off brand chargers damage your iPhone 5 battery life?

I'm thinking about buying an off brand charger from Amazon, and I was told that if you don't buy one from the Apple brand one than it can damage your phones battery life.

That is the ultimate question that nobody seems to know the answer to.
when it comes to DC power supply, the only thing that matters is voltage and current.
all mobile phones operate on 5 volts DC; however, the miliamps vary fom device to device. So the question is, can supplying the wrong amount of amperage to a phone damage its battery? In theory no, because the phone has on board voltage regulation.
but you also have to take into consideration other things such as how clean is the power?
noisy or " dirty " power can happen when cheaply made electronics are used in a power supply. If your battery charger does not have a well-built rectifier and AC filters, this causes noise and intermittentcy which can damage your battery.
so to answer your question, no. Using an off brand charger can't damage an iPhone, unless it's cheaply made

Yes that is correct. I read an article that says the same thing about buying off brand can cause damage to iphones. I do strong recommend buying only apple brand chargers for iphone.

Some can and in general it's safer to spend the extra money for something you know will work properly.