Example of semisimple Lie algebra which is not simple

Question

What is an example of semisimple Lie algebra which is not a simple Lie algebra?

Answer 1

As pointed out in the comments, you can take any two simple Lie algebras, like $\mathfrak{sl}_5$ and $\mathfrak{so}_8$, and consider their direct sum $\mathfrak{g} = \mathfrak{sl}_5 \oplus \mathfrak{so}_8$. Then $\mathfrak{g}$ is semisimple but not simple.