Bluetooth 4.0 Low Energy support on Sony Xperia Z5 or Z5 Compact
The Xperia z5 does support BLE, however with Android 5.1 and 6.0 I have been having enormous issues with it. Bluetooth regular profiles have been fine for me (audio mostly) but other people are seeing issues with connecting to car kits and the like.

I have an Xperia Z5 Compact, unlocked and unmodified. I have trouble connecting to my Pebble Time watch (basically will not work at all), TrackR tags keep losing their connection and my Jawbone UP3 frequently is disconnected. As I say though audio to my Bluetooth headphones, portable speaker and home Amplifier are all fine.

I do believe the issue is with the phone, and hope very much for a swift update to solve this because it is very annoying.