What happens if I don't use a relay for 5V pump
You should put a resistor in series with the led to limit the current.

The IO pins cannot source enough current to run the pump without damaging themselves. That's why you need a buffer of some kind.

The extra components in the relay module are a transistor to do the actual switching and a reverse-biased flyback schottky diode in parallel with the relay coil. The flyback diode is required to absorb the voltage spike generated by the coil getting switched off and acting like an inductor. 

You can use a transistor to switch the motor directly assuming you can find one that can handle the current draw. If you do then you absolutely will need a flyback diode on the motor to avoid damage to the transistor.