A new perovskite-related oxide with the LaBaCuCoO5.2 composition has been stabilised. Its structure can be described as formed by the recurrent intergrowth of two alternating blocks of YBaCuFeO5 (2ac, i.e., two-fold perovskite superlattice) and YBa2Fe3O8 (3ac) structural types. From the starting material LaBaCuCoO5.2-delta (delta = 0), the rigorous control of the oxygen content has allowed the stabilisation of three new five fold perovskite-related superstructures with the compositions delta = 0.4, 0.8 and 1.1, which can also be described as recurrent intergrowths of two blocks showing 2ac and 3ac periodicity. The reduction process takes place through the 3ac periodic blocks, when 0 < delta < 0.8. Further oxygen decrease seems to involve the 2ac periodic blocks made up of pyramidal layers, giving rise to infinite layer units. The stability limit for these fivefold superstructures is delta = 1.1. In agreement with this the as-synthesised materials constitute an example of topotactic reaction, since their basic structure is kept through the reduction process.