If the roots are $x = ± 5i$, then the factors must be $\left(x − \left(3 + 5i\right)\right)$ and $\left(x − \left(3 − 5i\right)\right)$.

Use the factors to write an equation.
$\left(x − 3 + 5i\right)\left(x − 3 − 5i\right) = 0$

Multiply.
$\left(x − 3\right)^{2} − 25i ^{2} = 0$

$x^{2} − 6x + 34 = 0$