How to Spot fake iphone 5 battery?

Let Apple replace the battery. No worries about a fake one and a warranty on the exchange of the battery.

If you do that on your own, Apple will not service the phone anymore, even if you would be willing to pay the service fee.

Out-of-warranty repair service
If your repair isn’t covered by Apple’s One Year Limited Warranty, AppleCare+, or AppleCare Protection Plan, your iPhone might be eligible for out-of-warranty service. For example, liquid damage isn’t covered by warranty but might be eligible for out-of-warranty service. Some damage isn’t eligible at all, for example if your device has been broken into multiple pieces. See Apple’s Repair Terms and Conditions for complete details.
Read Apple’s Repair Terms and Conditions

Model	Out-of-warranty service fee	Battery service*
iPhone 6 Plus	$329	$79 *available only if battery fails Apple’s diagnostic test
iPhone 6	$299
iPhone 5s, iPhone 5c, iPhone 5	$269
iPhone 4s	$199
iPhone 4, iPhone 3GS, iPhone 3G, Original iPhone	$149

Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing and may be less than the service fee listed above. Pricing and terms vary for service through an Apple Authorized Service Provider.

copied from Service Answer Center - iPhone

That's easy. Every battery you can buy is either fake or taken from another iPhone (i.e. used).

Apple does not sell iPhone parts at all, including batteries.

If you haven't already opened up the phone, make an appointment at the genius bar. Battery replacement is ~$70. Since you have an iPhone 5, you may even get a replacement for free if it falls under the iPhone 5 battery replacement program.

https://www.apple.com/support/iphone5-battery/

I want to buy a new battery can u help about that battery original or fak

Which part of @KiltedTim's response right above yours do you not understand?

Devapaul Johnny wrote:

I want to buy a new battery can u help about that battery original or fak

It's fake.