On surfaces with pg = q = 2, k2 = 5 and albanese map of degree 3

We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with pg = q = 2 and K2 = 5, which contains both examples given by Chen-Hacon and the first author. This component is generically smooth of dimension 4, and all its points parametrize surfaces whose Albanese map is a generically finite triple cover.