I don't have any type of insurance for my new iPhone 5. I bought it on Friday, December 7, 2012

Not sure what you are asking?

Is your charger dead? Phone dead?

These are not insurance claims, rather Warranty claims, and should be covered unless you damaged the items.

You can purchase AppleCare+ for your iPhone, but you must do within a month of purchasing it.

http://www.apple.com/support/products/iphone.html

If something is wrong with it, Apple will either fix it or replace it under warranty. You do not have to purchase any "insurance" for that.

All apple products have 1 year warranty. I've had apple products without apple care and still had things replaced or fixed. But what do you mean will you be able to exchange it for a charger...?

This is a warranty issue. Call Apple Care now or go to an Apple Store and get it replace. However you should get the mobile insurance for your device now from your provide, you usually have 30 days. Just do it. It'll be the best thing you can do. ➕