The locus of lines in Q leading generically to marked numerical Godeaux surfaces with torsion group ℤ/5 is birational to a union of two copies of ℙ1. The procedures gives two parametrization homomorphisms from Sa to the coordinate ring of a ℙ1 × ℙ1, where the image of each map gives a point in Q whose connecting line is completely contained in Q and leads generically to a ℤ/5-Godeaux surface.