C5 couples the transition of the '1602 CTS line (high to low) to the '328P's /RESET input.
Resetting the '328P remotely via the CTS is the way the Arduino Bootloader is activated so that you can load sketches from the Arduino IDE. When communications are first established, the CTS line is toggled in order to trigger a reset.
C5 is necessary because the CTS will remain LOW for a longer period of time than would be desirable to hold the '328P in a reset state.
The capacitor will pass only the edges of the signal so that the reset only happens at the moment the CTS output goes low.
We all learned that "Only AC can pass through a capacitor" but that's an overly simplistic explanation. A more accurate picture of what happens in a case like this is the following:
i = C*dv/dt, where i is the current flowing through the capacitor, C is the capacitance and dv/dt is an expression that describes the time rate-of-change of the voltage across the capacitor. You also have to consider another property, which is q=C*V.
In plain English, if a capacitor is less than fully charged, and a voltage is impressed across it through a resistance, a current will flow through it, but that current will decrease as the capacitor "fills up." When it can hold no more charge, the current will fall to zero.
In the case of this reset circuit, the empty capacitor presents a very low impedance (practically a short-circuit) that "pulls down" the logic level of the '328P reset input for a few milliseconds until the cap charges through the pull-up resistor on the reset input. When the CTS line goes back to the HIGH state, the capacitor will discharge through the pullup resistor, readying it for the next falling edge of CTS.
If you want to learn more about the math behind the inner workings of capacitors, you can start here:
https://en.wikipedia.org/wiki/Capacitance