Hi Hope,
First please help check my understanding your question: iPhone3 plug in TPS2511 is ok, plug in iPhone5, display "'charging with this device is not supported' on the screen and What's the voltage at this moments on D+/D-, if set TPS2511 to 5W mode, iPhone5 works good, right? Acctually, we have tested one pc iPhone5 in our Lab, it looks work good with TPS2511.