Cartan subalgebra of ${\frak so}(5)$

Question

I would like to find effectively the Cartan subalgebra of ${\frak so}(5)$. Does anybody knows how to proceed?

Edit: I don't want to start from the simple roots and then derive it. I would like to do the pedagogical procedure, starting from the cartan subalgebra and identifying the simple roots.

Answer 1

For the Cartan subalgebra of $B_2$ (in fact, for all classical simple Lie algebras), see this handout. Here $B_2$ is the root system of $\mathfrak{so}(5)$.