how do I close out all the open apps on my 5S?

iOS 7 How to Close Apps

Double Tap the Home Button... Then swipe the App (not the icon) Upwards... Tap the Home Button when finished.

More Info on Multitasking Here > http://support.apple.com/kb/HT4211

double tap the home botton and then throw away the open app. to close it 🙂