The locus of lines in $Q$ leading generically to marked numerical Godeaux surfaces with torsion group $\mathbb{Z}/5$ is birational to a union of two copies of $\mathbb{P}^1$. The procedures gives two parametrization homomorphisms from $S_a$ to the coordinate ring of a $\mathbb{P}^1 \ \times \ \mathbb{P}^1$, where the image of each map gives a point in $Q$ whose connecting line is completely contained in $Q$ and leads generically to a $\mathbb{Z}/5$-Godeaux surface.
The object precomputedTorsZ5Line is a method function.