How can I run HC-05 on 8MHz Pro Mini?
Basically Arduino Uno Is working On 5v Voltage Level so you can Directly connect the HC-05 Bluetooth module to it using it 4 lines VCC,TX,RX,GND.

But in Pro mini 3.3 V level due to you need to Generic 3.3V To 5V 2 Channel Logic Level Converter Bi-Directional Module

using this you can easily convert the vlotage level.

if you have to make using simple component also using 

SparkFun Logic Level Converter - Bi-Directional