Find the formula of halide of a metal whose succcessive ionization energies are x , 2x , 5x , 20x , 25x kJ per mole respectively

The metal is most likely to form MCl₃ type of halide since +3 oxidation state of metal is most stable among all the oxidation states.

The successive ionisation energy is increasing for metal but there is a sudden sharp increase in fourth ionisation energy   (5x$\to$20x) as compared to the regular increasing trend. This shows metal is extra stable in +3 oxidation state that is why fourth ionisation energy is abnormally high. Thus it will form MCl₃ type of halide.