Negative voltage using boost converter
Think of it like a single-action pump. The capacitor blocks DC voltage, so the only thing going through is an AC waveform (\$\approx V_{OUT}\$ peak-to-peak, as seen at the switching node).

On the falling edge, current is sucked through D1, and during the rising edge, current is pushed through D3. Since current is being pulled from the top side of C5 and being deposited at ground, a negative voltage develops across C5.

D2 and R10 are then used to control the output voltage in the same way that D5 and R11 are used to control the positive output voltage.