And how did transfer your contacts before? Sorry but it doesn't look too good, it was so easy to transfer your contacts to Google using iTunes, but as far as I know fir that you need your iPhone, so if you didn't do it back then and after you set your S5 never transferred them to Google, then you must use this as a learning experience and begin from scratch.
So first thing you should do is be sure that when you are creating them you are selecting your Google account and not the phone or Sim card, this will prevent something like this to happen again, but again I'm wondering how you transferred them to your S5 before.