If these LEDs are in series, then you add the voltages of each LED (2V sounds low, unless they're red/orange/amber). 2*5 = 10V across the LEDs. Since your power supply is 12V, you have to absorb those extra 2 volts when running 20mA through the circuit. Using the equation Voltage = Current * Resistance, you use 2 = 0.020 * R. R = 100 ohms.
The calculator incorrectly instructs you to use a 120 ohm resistor (it goes for the NEXT highest resistor, even if the calculated resistor matches exactly).
A 1/8 watt resistor just means that it can handle the heat from 1/8 of a watt passing through it. There is no harm in using a higher-wattage resistor.