I have been playing around with the AT commands of HC-05 recently. Here's what I have found,
This will show HC-05 as an INPUT device(GAMEPAD) on your system. We are able to pair to the gamepad but not connect to it.
On the datasheet they also say it can be configures as a Master device aswell.
where, 0 is for slave, 1 for master, 2 for slave-loop
But when I configured it as a Master device it stopped showing on the bluetooth devices list.