how much does it cost to repair backlight of iphone 5 in warranty with water damage

If the iPhone has suffered water damage, the warranty is now void. If you have AppleCare+ coverage, the cost for service will low; in the US it's $49. If you do not have AppleCare+ on your iPhone, Apple reportedly now will replace the screen, if that would address your problem, in an iPhone 5 for US $149. Availabllity of repair services may vary by country, so call Apple Support or visit an Apple Store and ask for information. If Apple is not currently offering screen replacement service in your country, they will replace the entire iPhone for a flat fee. See the Service Pricing section here:

http://www.apple.com/support/iphone/service/faq/

There are independent iPhone repair services that may be able to do the repair for less than Apple's out-of-warranty charge. Do a web search for "iPhone repair". Note, though, that if you elect to have the iPhone serviced by an unauthorized shop, all further warranty and support from Apple will be voided.

Regards.

Forum Tip: Since you're new here, you've probably not discovered the Search feature available on every Communities page, but next time, it might save you time (and everyone else from having to answer the same question multiple times) if you search a couple of ways for a topic, both in the relevant forums and in the Apple Knowledge Base, before you post a question.