Nick_Pyner:
The backboard probably states 3.6 - 6v quite clearly, thereby strongly implying that 3.7v is sufficient but 2x3.7 is probably too much. I don't suppose a coin cell has enough power to run an HC-05.
The backboard says 5v. And it should support around 5~7v input.
I am only using the coin cell for powering the pro mini, and it works fine.
But what about the hc-05?