Is it possible to use a dual rail power system to power op-amp which is designed for a single supply?
It won't work as you wish - the ground in the circuit must be connected to the most negative supply rail i.e. the -5V rail. You might be able to couple your audio to the circuit thru a capacitor but it could be quite noisy. This could be overcome with an audio coupling transformer but, maybe just try running it from a single 5V rail (yes it will work at 5V or even 4V for some versions) then consider using a boost regulator to give you a clean (after extra filtering) 10V or 12V.