Apple doesn’t yet sell an unlocked version of the iPhone 5s. However, if you want one, buy a Verizon model. They’re GSM-unlocked, and you can use them with AT&T or T-Mobile by popping in a SIM. (They won’t ever work on Sprint — but why would you want them to?)
If you’re not into Verizon, and don’t mind paying full price, you can go to an Apple retail store and ask for the Verizon model “device-only” or “without activation.” If they have it — still likely to be a big IF for a few weeks — they’ll sell it to you right off the shelf without enrolling you in anything. You don’t need to be, or become, a Verizon customer.
Alternatively, you could buy the phone at full price, with a month-to-month contract, on Verizon’s web site or in one of their stores, and then immediately cancel service if you don’t want it. (Or you could buy a subsidized plan and pay the contract-breaking fee.)
You can do the same with the iPhone 5c, though that model you can also buy officially unlocked from Apple’s web site or at a retail store. The unlocked model will never work with Verizon or Sprint, but it will work with any GSM carrier.
If you did buy the phone for another carrier:
The AT&T version is sold locked, but AT&T will unlock it if you have completed your subsidized contract, bought the phone at full price (contract-free), or have fully paid off the phone in their “Next” layaway plan. It requires filling out a form, and then erasing and restoring the phone using iTunes.
The T-Mobile version is sold locked, but T-Mobile will unlock it if the phone is fully paid and you have used it for 40 days with them. (If you get the phone from Apple rather than T-Mobile, I think it comes unlocked in the box, but then locks itself for T-Mobile when you activate their SIM card for service.)
The Sprint version is sold locked, and they will unlock it for international carriers only after 90 days. They won’t unlock it for domestic carriers ever. Don’t use Sprint.
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