AC 20V to DC 5V converter with zener diode question
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Various options.


(a) Your circuit. Note that C1 charges up on positive half-cycles but the LED discharges it continuously. You need to take this into account in your calculations. R1 is conducting on negative half-cycles with current through D1 so that's a waste of energy.
(b) Moving the diode to the left solves the negative half-cycle problem and cuts power consumption in half. It doesn't solve the LED problem and the voltage on C1 will droop on negative half-cycles.
(c) solves the droop by providing a high-voltage DC supply that is regulated by the Zener. We still haven't worked out the R values though.
(d) It's not clear why you don't just use this arrangement. Maybe you need to avoid flicker.


Assuming your 20 V supply is 20 V RMS then the peak voltage should be about 30 V. Working with the RMS value and assuming you want 20 mA through the LED we can work out the following:

$$ I_{R1} = \frac {20-5.6}{2k} = 7.2 \ \mathrm{mA} $$

Already we don't have enough current for the positive half-cycles. Having no useful current for the negative cycles makes the situation worse.

Rethink your circuit and the requirements. Then do the design. Update your question if required.