I'm trying to find a discrete subgroup $\Lambda$ of $PSL(2,\mathbb{Z})$ such that $$\mathbb{H}/\Lambda \cong \Sigma_{0,5}$$ where $\Sigma_{0,5}$ is the five punctured sphere.
I know that, if $\Lambda=\Gamma(2)$, then $\mathbb{H}/\Lambda$ is the three punctured sphere $\Sigma_{0,3}$, this is proved by counting the orbits of $\Lambda$ on $\mathbb{Q}\cup\{\infty\}$. With this in mind, I've tried the same approach with different principal congruence subgroups $\Gamma(n)$, but none of them has 5 cusps as I require.
Maybe I'm missing something but I've run out of ideas. Could somebody point me in the right direction?
$\Gamma(n)$ is defined as the elements in $PSL(2,\mathbb{Z})$ congruent with the identity modulo $n$.