How to make the motor car move left-forward / left-backward/ right-forward/ right-backward
Regarding the pins - I wanted to find out the physical (hardware) connections.

Pending an updated answer I presume the EA and EB will set the speed for two motors and EN2/EN3 and EN4/EN5 control the direction of the motors. If that's the case you could make the car turn sideways but changing the speed of only one of the motors. For example:

void forwardLeft(void) { 
  analogWrite(EA,128); //speed 0 - 255
  analogWrite(EB,255); //speed 0 - 255
  digitalWrite(EN2,LOW);
  digitalWrite(EN3,HIGH);
  digitalWrite(EN4,LOW);
  digitalWrite(EN5,HIGH);
}


I assume that EA is the left motor and EB is the right motor. This will make the right one rotate twice as fast as the left one so the car should go forward, but also turn left. If you keep this running the car should end up going in a circle. By making the 128 lower you will change how fast the car is turning.

The other functions should be similar.

Caveat emptor - of course this will mean nothing if the beginning assumptions are incorrect.

EDIT
Can't figure out why it doesn't work without having the thing in my hands. Have not found a schematic for that board, but intuitively it should work as described above.

Things you can do to try to figure out - try different numbers instead of 128, the speed of the motors might not vary linearly with the voltage. What you need to obtain is to have one motor go twice as fast as the other one and in the same direction. That should turn the car around.