Also to add. This device does not actually have any audio involved. It controls say the pitch of the audio or the rate of an lfo in the modulation of the audio. So it's all DC right? Not sure if this matter.
Yes it matters. It means you can't use the simple circuit I showed to give a DC bias.
The synth operates at -5 to +5
So are you expecting the Arduino to output voltages over the range -5 to +5? That is a lot more complected.
What sort of resolution do you need?
When you put an analogue voltage into a digital system it turns that voltage into a number. For the Arduino those numbers go from 0 to 1023, to represent an input voltage of 0 to 5V. Is this granularity good enough for you?
When an Arduino outputs a voltage it only has a granularity of numbers 0 to 255 to represent voltages 0 to 5V.
These last two factors can be changed but only by adding external hardware.
After the Arduino it gets put into an attenuverter which attenuates and inverts the 5v signal from the Arduino. Back to -5v to +5v. Then goes back to the synth for control.
So you have one of these attenuverter already or are you hoping to build one?