That coil has a resistance of 168R so for a 5V coil you get 30mA. The LED is normally driven at 20mA, if so that would damage the arduino because 30 + 20 = 50mA = too much.
In theory you could use 10mA for the LED but you need to restrict it to 5mA if you want to drive the whole load safely. You also need a diode across the coil.
Why will you not use a transistor!!!!!