  Let k be an algebraically closed field of characteristic 0. The question of
irreducibility of the punctual Hilbert scheme Hilb_d P^n and its Gorenstein
locus for various d was studied in [CEVV8, CN9, CN10, CN11]. In this short
paper we prove that the subschemes corresponding to the Gorenstein algebras
having Hilbert function (1,5,5,1) are smoothable i.e. lie in the closure of the
locus of smooth subschemes. Among the Gorenstein algebras of length 12 the
smoothability of algebras having such Hilbert function seems to be the most
inapproachable using non-direct tools e.g. structural theorems.
