You'll have <18mA for each LED with a 270-ohm series limiting resistor at 5V.

LED current = Vcc - Vled/R. Vled is the voltage drop of the LED. R is the series limiting resistor.

With Vcc = 5V, Vled = 1.2V and R=270, then (5V-1.2V)/270 = ~14mA.

8 x 14mA = ~112mA total for 8 LED's. Should be fine. Most LED's will glow pretty good with just 8-10mA.