Can iControl 11.5 API work on BigIP 10.2

The API is backwards compatible, but in newer versions of the API, methods that existed in 10.2 may no longer be present in the online API reference, while newer commands that are listed won't work. Just make sure you read the fine print on each method. Any method ending with _v2 will likely not work with 10.2.

So for python/ruby, or if you are building the soap calls yourself (brave!) it shouldn't be an issue. If you are using a library, you should use the one for your version.