You have the following situation:
Arduino with DAC generates 0V - +5V sin wave (2.5V +/- 2.5V).
The output should be -2V - +2V sin wave (0V +/- 2V).
Arduino with DAC + C1 + R1 + R2 (all elements are in series).
- C1 + R, where R = R1 + R2 is a high pass filter
- R1 and R2 is a voltage divider with the gain of 0.8 V/V
- can be used if DAC is able to source/sink enough current
Arduino with DAC + opamp buffer + C1 + R1 + R2 (all elements are in series).
- use in case your DAC is not able to source/sink enough current
Arduino with DAC + opamp subtractor + C1 + R1 (all elements are in series).
- C1 + R1 is a high pass filter
A single opamp in a configuration of the subtractor takes care of your equation:
Vo = (Vi-2.5) * 0.8
Look here: http://www.mtcmos.com/subtractor/ . You would like to use the configuration at the end of the article, that is, the left from this picture:
- R2/R1 = 0.8
- V1 = 2.5V
- V2 = Vi
So you get:
Vo = 0.8 * (Vi - 2.5)
You may also refer to this e-book https://payhip.com/b/5Srt. The subtractor circuit explanation is a bit improved there (the core is the same), but you also find other configurations explained.