jmc

We complete the square. We can square $x-\frac{5}{2}$ to get $x^2-5x+\frac{25}{4}$, so $x^2-5x={\left(x-\frac{5}{2}\right)}^2-\frac{25}{4}$. We see that $k=\boxed{-\frac{25}{4}}$.