What resistor should I use after changing this LED from using 220v to using 5v arduino?
Typical capacitive dropper setup. They use the resistor and capacitor to drop the 220V down to the led needs.

Cut the existing resistor and cap off. Replace the resistor with r = (V source - Typical Forward Voltage) / typical forward current for your color led.

Assume 5V Vs, 20mA If.