You can try either of the following. Reset all settings - Settings > General > Reset > Reset All Settings [It should say the following (This will reset all settings. No data or media will be deleted.)]
Or
Hold the top power button and the home button until the Apple logo appears.
Also, I read that their is an issue with Bluetooth on the 64bit iOS 7 (iPhone 5s), iOS 7.1 is supposed to fix it when they release it (that May or may not fix your issue).
Hope you get it going, I tested it with my friend's 5s when it first came out and it worked then.
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