How to calculate resistors for transistor driver circuit
R2, in series with the LED, is (Vcc - Vled)/I = (5 - 1.4)/0.1 = 36 Ohms.  However, since the Absolute Maximum current for the LED is 100 mA, I'd probably use 42 or 47 Ohms to reduce the current a bit.

The base current should be collector current/Hfe = 0.1/30 = 3.3 mA.  The required base resistor is then (3.3 - 0.7)/.0033 = 788 Ohms.  The resistor value should be a little less to ensure sufficinet base current to keep the transistor in saturation, so 510 or 620 Ohms should be fine.