A dedicated cable, of course, has to go all the way back to the circuit panel. Ask trusted friends or family for contractor recommendations. The contractor will perform an installation inspection to ensure the installation was done correctly and the system functions properly. If it does not then use the spare wire for the blue wire and restore the red. Since you have 5 wires I would go with an conductor wire to give you extra wires in the future.
If your home or business does have a duct system and you want to install a ducted central air conditioner, the existing ducts may require repairs or alterations to support the new system.
So I recommend you either go to school and learn about it yourself and fix it yourself or pay a contractor to work on it for you. If it hooks to the compressor and it burned up you could have other problems also that caused the part to burn up.