Bluetooth HC-05 is not working.

Yes, it looks like you figured that out.
You can get the bare module that goes on the board separately, but best bet may be to buy the board complete with the module.
I saw this listing that appears they have bare modules, bare boards, and combined board with module: http://www.ebay.com/itm/1-5-10PCS-HC-06-HC-05-30ft-Wireless-Bluetooth-RF-Transceiver-Module-RS232-TTL-/282221351296