cattledog:
Do you have the HC05 paired with the PC's Bluetooth? You may not be able to see it on a COM port unless it is first paired.
I don't think that is right. Surely, PC needs to know what port Bluetooth is on in order to pair with it. Also note that Bluetooth can sometimes be seen on two ports. This has never happened to me, but I guess they are for transmit and receive. Things can get rather messy with Bluetooth on a PC. I think using Android is a much better option.