I have paired with success the two devices.
Here is the answer I got from BSX Insight :
"Thank you for writing to me at BSX Technologies! I am happy to assist you with your inquires. There is not an issue with your devices. The Fenix 5 does not include a start and stop feature at this time. You will need to start and stop your BSXinsight from the BSXinsight mobile app.
Your Garmin Fenix 5X does allow you native viewing of your SmO2 and tHb from the watch without any updates. Your BSXinsight will create a Garmin FIT file once you dock and sync. At this time Garmin does not accept the file."
Thus it could be nice from Garmin to achieve the integration of the BSX insight with the Fenix 5X :
- Start/stop function
- SMO2/tHb data recording on Fenix 5X /Garmin Connect