First note that . So we want to know when a square can be congruent to five times a square (mod 7).

The only squares (mod 7) are 0, 1, 2 and 4. And the only way for one of these to be congruent to five times another one is if they are both 0. Thus a and b must both be congruent to 0 (mod 7), and so and must both be congruent to 0 (mod ).