Why would ou think you are allowed to unlock an 5S, you have to be a paying customer using the handset for at least 6 months. Seeing as the 5S hasn't even been out 6 months your not going to get this unlocked through EE.
They have policies for reasons they won't bend them for you.
They won't even consider unlocking it.
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EE Contact Details...
150 from EE Mobile 0800 956 6000 (Option 5) from any other phone 0800 079 8586 Home Broadband & EE TV