Voltage regulator output ripple
The impedance of a capacitor is \$ 1/(2 \pi f C)\$ so a 1000µF cap will have 160 ohms impedance at 1Hz.

Your regulator has an output impedance too. This is due to the internal feedback loop which adjusts the output transistor drive to respond to changing load currents. This loop is not infinitely fast, and it does not have infinite gain, so it will not hold the output voltage perfectly at the set point, but at low frequencies output impedance is pretty low. Say, 0.01 ohms.

Thus, considering the two impedances in parallel, the regulator will control the output completely at 1Hz. The cap only comes into play at much higher frequencies.

The low-frequency output ripple will depend entirely on regulator noise, and the input ripple divided by regulator ripple rejection.

Why do you need 1mV ripple on 5V?