Since the 386 is socketed in V5, here's a no-soldering hack to reduce the gain:
Power off the BitX before starting...
1. Observe which end the notch on the body of the 386 is facing
2. Remove 386 carefully from socket (i.e. use tiny screwdriver pull up chip body incrementally back and forth from each side)
3. Gently lift either pin 1 or 8 90 degrees so it is horizontal. These are the pins closest to the notch, that is, in each line of four pins, the pin at the end of each line closes to the notch.
4. Reinsert the 386 into the socket in a straight down manner until firmly in place, ensuring that all remaining 7 pins go into their proper slot (and don't bend accidentally due to misalignment). Make sure that the notch on the 386 is facing the same direction that it was when you removed it.
Try it out by turning on the BitX - there will be less hiss added to the audio (especially noticeable in headphones)