In this method we use the derivative f'(x)=3x^2-2 and apply the iteration:
x1=x0-f(0)/f'(0) initially. Put x=0 initially: -(-5/-2)=2.5 is x1.
Plug in x1: x2=2.164...-f(2.164...)/f'(2.164...)=2.097...
x3=2.094555232, x gets closer to 2.094551482 fairly rapidly.