converting 0V - 10V to -5V - 5V
Assuming that your control voltage is not (necessarily) varying much, such as when it commands a constant frequency or level, then there is no passive circuit which will do what you want. Instead, you'll need an op amp and some resistors. This circuit







simulate this circuit &ndash; Schematic created using CircuitLab

will do the job.

Fortunately, you have all 3 voltages available.

Accuracy will depend on 2 things: the accuracy of your 5 volts, and the accuracy of the resistors.

Resistors first. If you use readily available 1% resistors, the output will be accurate to about 1%. If you need better accuracy, you'll need more precise (and more expensive) resistors, but 0.1% resistors are fairly cheap and should be more than adequate for synthesizer work.

Now the 5 volts. The circuit is called a differential amplifier, and the level shift produced by the 5 volts is, obviously, equal to the value of the 5 volt input. If your system actually provides 4.9 volts, this is what you'll get for a shift.

For this application you'll want an older op amp such as the specified TL081. Be aware that many newer op amps are not rated for the voltages you're using, so be careful. Before you get an op amp, check the data sheet to make sure that it will work with +/- 12 volt supplies.