Where did you hear such a thing? Apple does not have (and never has had) any kind of trade in nor buy back program. I've never heard of a carrier offering any such thing either.
Note that a 16GB iPhone 5 with new carrier contract (or upgrade eligability with your current carrier), goes for $199.00. This is not a "trade in" deal - nobody wants your old phone. This is the price with a new 2year contract commitment.
Since you don't provide any useful information, like who is making this offer, where, etc. we can't say.
My gut, though says that the answer is either: No.
You have misunderstood something, since in the US, you can get an iPhone 5 for $200 (or less) by signing a 2 year contract with one of the major carriers here. The price is subsidised by the carrier in exchange for contracting for service with them.