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It depends on how elaborate the new supply should be. I would simply
use voltage divider (two 1k resistors) in series connected to the 12V power supply and a capacitor (10uF will do) in parallel with one of the resistors. This would provide +/-6V if you consider the resistor midpoint to be your new 0VDC.
If you really want to bring the voltage down to +/-5V, just put three Si diodes in the positive end of the power supply. This will drop the 12V down to 10V so the divider will provide +/-5V.
Depends on how much current you need. You can use a simple 5V linear regulator to generate the +5V, then use a switching converter to generate the -5V. A suitable -5V converter can be had from an ICL7660 or MAX687. For higher currents, it is probably easier to get a DC-DC converter such as a Vicor or something similar.
what current are you after?for a small value(100mA) an integrated regulator it's a easy way.for larger values(amps) try to look for an active voltage divider.it's a schematic which transforms the input voltage(say 10v)in a simetric voltage(+/-5v) using some transistors.it also stabilize the current.
Are you intending on running the power supply from mains? If you are buy a transformer with two secondary windings, one can be used for the +ve voltage the other for the -ve. Then bridge rectify the output and smooth it with a capacitor. Use three fixed coltage linear regulators to provide your different voltage levels. Standard ones are good for 1A which should be plenty for your op-amps.