Polycrystalline HoGaMnO5, ErGaMnO5, and TmGaMnO5 oxides have been first prepared by soft chemistry procedures followed by high oxygen pressure treatments, to stabilize Mn4+ cations. Their crystal structures and magnetic behavior have been studied at room temperature and 5 K by neutron powder diffraction (NPD) data in complement with magnetization measurements. RGaMnO5 are orthorhombic, Pbam space group, and their crystal structures contain infinite chains of edge-sharing Mn4+O6 octahedra, interconnected by pyramidal Ga3+O5 and RO8 units. For R = Ho, a = 7.2810(4), b = 8.4526(4), and c = 5.6668(3) Å; for R = Er, a = 7.2575(3), b = 8.4357(3), and c = 5.6613(2) Å; and for R = Tm, a = 7.2438(3), b = 8.4124(3), and c = 5.6509(2) Å, at room temperature. Above 300 K the reciprocal magnetic susceptibility follows a Curie-Weiss law. In the paramagnetic region, a positive Weiss constant suggests the presence of ferromagnetic interactions, which have been investigated by low-temperature NPD for R = Er, Tm. The 5 K patterns show a detectable long-range magnetic ordering over the Mn and R positions, ferromagnetically aligned along the x-direction.