(Joint work in progress with T. Papazachariou) K-moduli spaces provide a canonical parametrization of K-polystable Fano varieties, but they are rarely accessible in concrete terms. In this talk, I will describe an explicit example in dimension three. I will consider the Fano threefolds in Mori-Mukai family №3.5, which can be realised as blow-ups of P1xP2 along curves of bidegree (5,2). I will explain how the K-stability of these threefolds is determined by the classical GIT stability of the corresponding curves. This leads to an explicit description of the K-moduli space as a GIT quotient and yields a K-classification of all members of the family.