BALTIC-WAY 1998 Problem 2

A triple of positive integers $(a, b, c)$ is called quasi-Pythagorean if there exists a triangle with lengths of the sides $a, b, c$ and the angle opposite to the side $c$ equal to $120^{\circ}$. Prove that if $(a, b, c)$ is a quasi-Pythagorean triple then $c$ has a prime divisor greater than 5 .