### Trying to find prime factorization of ideals in number fields

Let $L=\mathbb{Q}(\sqrt{-5}, i)$ and $K=\mathbb{Q}(\sqrt{-5})$. Let $O_K$ and $O_L$ be the rings of algebraic integers of $K$ and $L$. It can be checked that

$$2O_K=\langle 2, \sqrt{-5}+1\rangle^2 $$

I want to find ~~out ~~the ~~prime ~~factorization of the ideal ~~generated by $2$ and $5$ ~~$\langle 2, \sqrt{-5}+1\rangle O_L$ in ~~$O_K$ and ~~$O_L$ ?

~~How ~~The problem I am having is this. I don't know the syntax for the ideal generated by $\langle 2, \sqrt{-5}+1\rangle O_L$.

What to do ~~this ~~?