There's nothing more horrifying than a frozen screen when you need to open an app, stat.
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This has been happening to more than a few users who've upgraded to iOS 9—this might be symptomatic of a larger issue (your 5c just might not be able to handle the update). But thankfully, there's something you can do about it.
First, double tap your home button—if you were already in an app when it froze, swipe up and close out of the app; it could just be the app's fault, and it hasn't updated properly for iOS 9 and is causing your grief. (If you update apps manually, make sure to go through and do so.) Then hit your homescreen, and hopefully all will be well. If that doesn't work, trying holding down the Sleep/Wake and home button at the same time to restart your phone.
