The equation $(k-5)x=k-7$ has no solution when:

If $k$ ≠ 5 we may divide and get the single value $x=(k-7)/(k-5)$. If $k=5$ the equation becomes 0 · $x=-2$, which no value of $x$ can satisfy. (At $k=7$ it becomes $2x=0$, which does have the solution $x=0.$)