This is a problem involving colligative properties. For problems involving freezing point depression, the formula is as follows:
Tfp,solvent - Tfp,solution = iKfm
For KI solution, the solvent is water. So, the freezing point of water, Tfp,solvent = 0°C. The i is the number of ions dissociated. In this case, i = 2 (1 for K⁺ and 1 for I⁻).
0 - Tfp,solution = (2)(1.86 ºc/m)(5 m)
Tfp,solution = -18.6°C