Unlocked 5s won't connect to new carrier (docomo) data network
It sounds as though the issue resides in the LTE bands supported by the device. If the iPhone is model A1533 it will not support LTE bands: 6 and 9. A1533 is the model of most American unlocked devices. On Apple's LTE site it gives a list of each unlocked device, and the supported bands that has been organized geographically. iPhone 5S model A1453 is the correct model.