Please unlock my iPhone

ONly the carrier that the phone is locked to can unlock it.

YOu will have to contact Sprint and see if they offer unlocking.

It sounds like your phone is unlocked but your using it on an unsupported carrier. China Telecom and Unicom are the 2 supported carriers. If using on any other you will need to figure out how to get them to work.

Note that some features on a unsupported carrier may not work.

Sorry, Apple doesn't unlock phones only the CARRIER does, which in your case is Sprint.

Here's the deal, Sprint controls whether your sim slot is unlocked or not, not Apple or anyone else. Fact is, Sprint absolutely will not authorize the unlocking of your sim slot unless you are a customer in good standing. So, either sign up for service with Sprint & then request the sim slot be unlocked, or sell the phone. If not unlocked, it will be useless to you in China. Apple can't/won't help you.

No, Apple didn't let you down. If you had gone to an Apple Store you could have purchased an UNLOCKED iPhone 5 and used it now. Instead you chose to go to a Sprint Store and purchase a no contract LOCKED iPhone (Sprint doesn't sell and unlocked iPhone 5). Or, better yet, you could buy an iPhone in China.

You tried to save some money by going around the system and you did not do your homework. If you sign up for Sprint service for six months you can then apply to unlock the GSM side of the phone.

Your best bet at this point is to sell the iPhone 5 to a Sprint user and use the proceeds towards buying an iPhone in China.