How would you know if your iPhone 5s is made in Japan? And what's the model number at the back cover?

the back should state it's designed by Apple in California and assembled in China,

and you can verify the seiral number with Apple using the link below

Find the serial number of your Apple product - Apple Support

No iPhone, iPad nor iPod Touch has ever been assembled or manufactured in Japan. Almost all Apple iOS devices are assembled in China, but some have been or are assembled in Taiwan (same manufacturer but FoxConn's parent company has over a dozen production facilities, most in China and a few in Taiwan).

For an iPhone destined to be sold (not made) in Japan, the model number in Settings->General->About->Model will have a J before the /.

For example: MC605J/A

And would generally be locked to a Japanese cell carrier. Though some carriers do now offer unlocking,

And yes, the camera shutter sound cannot be turned off on an iPhone meant for Japan.

The iPhone is not made in Japan.