As the OP hasn't even told us how many (milli)Amperes he needs from the -5V, it might not even be practical for a 555 charge pump solution. Though given what little we have to go on, I would agree this is the most likely answers for now.
In my view you can generate both +5v and -5V from center-tap transformer approach and use relay's NC contact for +5Volt NO for -5V and common as a control signal going to your circuit......and control the relay coil for getting either voltages ..... In the Opamp Circuit you need to have +/- 5volt supply any how..... and in Charge Pump Circuit dose not allow you to drive the load more than 50ma......
Also if you want to choose NE555 timer IC pay attention on needed input voltage. Some other IC can make -5V from +5V. If input voltage is +5V then NE555 CMOS is needed.