Welcome to FT!
With no airline status and not flying premium class, you won't have any lounge access.
And neither of your credit cards will help you either.
There are a couple of paid access lounges landside, which means you have to exit and then come back in again. But five hours should be plenty, assuming you don't need a (transit) visa?
Take a look at the FRA website http://www.frankfurt-airport.com/con...t/lounges.html