Wifi won't be active unless you manually start it, or you completed an activity and have wifi set for auto upload, and those are things that won't happen when you are asleep. For BT, you can easily turn that off on the watch if you want.
I have found that on my FR935 leaving BT on if the phone is in the same room has no significant effect on the battery life, i.e. less than half a day difference across 2 weeks.. If the phone is kept in a different room and the watch disconnects, then all bets are off. I found it is important to make sure the two devices are kept close enough that they stay connected and the watch never has to go into searching mode. If I am going to be out of range of the phone for a while, I will turn off BT then turn turn it back on when I know the two devices are in range again. I had a similar experiences with my FR230. So no reason to think the F5x would fare much different.
Your mileage may very, but this is my experience.