We describe the moduli space of $\mathbb Q$-homology projective planes with 5 quotient singular points, the maximum possible case. In particular, we show that the moduli space has dimension 0.

We also present an Enriques surface having two different elliptic fibrations with a multi-section giving the same configuration of 9 smooth rational curves of Dynkin type $3A_1 \oplus 2A_3.$