How many cost a new original battery of Iphone 5 ?

Difficult for us to answer. We do not know where you are from and prices often vary between the different countries. I believe this applies to the USA but it gives you a guide.

Your one-year warranty includes replacement coverage for a defective battery.

You can extend your coverage to two years from the date of your iPhone purchase with the AppleCare Protection Plan for iPhone. During the plan’s coverage period, Apple will replace the battery if it drops below 50% of its original capacity. If it is out of warranty, Apple offers a battery replacement for $79, plus $6.95 shipping, subject to local tax. Apple disposes of your battery in an environmentally friendly manner.

The battery bad, not really what I expect, unless you often let the iPhone off the charger until it switches off on itself. That is very bad for a battery. Read some threads here what settings you can change to preserve battery life. Do not let it discharge under than say 20-25% left.

The easiest thing to do is buy a case with extra battery built in, like Mophie's Space Back. A review here:

http://arstechnica.com/apple/2014/03/review-mophies-space-pack-doubles-your-ipho nes-battery-storage-and-size/