Hey Zeig,
Sounds you're using the RF input on the TV as the source video, with audio back to your receiver? Or do you use outboard video sources, i.e. AppleTV, Cable or Satellite?
The BT device sends stereo, so will not deliver any surround sound encoded in the program.
Your 5.1 receiver most likely has a coaxial and/or optical input for multi channel playback. If only coaxial, there are optical to coaxial converters. Look for Vanco for options.
VZ's suggestion is a great solution, I will use it on car/truck applications. Thanks VZ!