One of the roots of $x^2-4x+5=0$ is $2+i$

$\Delta =b^2-4ac$

$={\left(4\right)}^2-4\left(5\right)\left(1\right)$

$=-4<0$

$\therefore$  roots are complex and conjugate to each other

$x=\frac{4\pm \sqrt{{\left(4\right)}^2-4\left(1\right)\left(5\right)}}{2}$

$x=\frac{4\pm \sqrt{-4}}{2}=\frac{4\pm 2i}{2}$

$x=2\pm i$