Hey there!
Mine has the exact same problem, the power button rattles when I shake it :/Some details of my phone are given below:
Colour: Gold
Model: iPhone 5s
Status: Factory Unlocked
Memory: 16 GB
It says designed by Apple california, Assembled in China.
I don't know what to do !!
APPLE PLEASE SOLVE IT, IT'S EXTREMELY ANNOYING !!
and Second my iPhone over heats over specific apps :/ it's a problem with many iPhone 5s users I know!
Please APPLE solve our issues! We are your loyal costumers !!!
Regards
Navid, 24000, Pakistan.