How can you block a call or certain phone number on I-Phone 5?

You have to be running iOS 7. Are you?

Until you upgrade to iOS 7 (which you would be wise to wait a few days to allow the mad rush to die down); Anyway, until you upgrade ot iOS 7, you can fake it by downloading a "Silent" ring tone, then creating a contact for this phone number specifying the Silent ring tone and no vibrate. The call will still come in, but the iPhone will not ring nor vibrate, so it will not be annoying you.

Google Search for "Silent ring tone" and you will find a silent ring tone and instructions on installing it.

Once you install iOS 7, I am told it has the ability to block phone numbers.

It does, which is why I asked if he was running it.

Update ur iphone to ios 7, press the phone app & go to recents call list, click the "i" sign right after each number list, scroll down to bottom select "Block this caller".