Do you have to pay for all games on iPhone 5?

No. As with all previous-generation iPhones and iPod touches, there are thousands of games available on the App Store that are free. The easiest way to find them is to go to the App Store, tap on "Top Charts" (the button with the star on it at the bottom) and browse through the top "Free" section, which (at the time of this writing) is the middle horizontal section. You can also tap on the "See All" link to the far right of this section to see all the top Free apps, rather than the preview shown.