Single crystals of (Ca1-xLax)10(Pt3As8)(Fe2As2)5 (x = 0 to 0.182) superconductors have been grown and characterized by X-ray, microprobe, transport and thermodynamic measurements. Features in the magnetic susceptibility, specific heat and two kinks in the derivative of the electrical resistivity around 100 K in the x = 0 compound support the existence of decoupled structural and magnetic phase transitions. With La doping, the structural/magnetic phase transitions are suppressed and a half-dome of superconductivity with a maximal Tc around 26 K is observed in the temperature-concentration phase diagram.