A multijunction solar cell comprising: an upper first solar subcell (206a,206b,206c,207) having a first band gap, and the base-emitter junction (207,206b) of the upper first solar subcell being a homojunction; a second solar subcell (211,212) adjacent to said first solar subcell and having a second band gap smaller than said first band gap; a third solar subcell (216,217) adjacent to said second solar subcell and having a third band gap in a range of approximately 1.3 to 1.5 eV and smaller than said second band gap; a first graded interlayer adjacent to said third solar subcell; said first graded interlayer having a fourth band gap greater than said third band gap; and that is constant at approximately 1.5 eV throughout the thickness of the first graded interlayer; and a fourth solar subcell (224,225) adjacent to said first graded interlayer, said fourth subcell having a fifth band gap of approximately 1.0 to 1.2 eV wherein said fourth subcell is lattice mismatched with respect to said third subcell; a second graded interlayer adjacent to said fourth solar subcell; said second graded interlayer having a sixth band gap greater than said fifth band gap; and that is constant at approximately 1.1 eV throughout the thickness of the second graded interlayer; a lower fifth solar subcell (232,233) adjacent to said second graded interlayer, said lower fifth subcell having a seventh band gap smaller than said fifth band gap wherein that said fifth subcell is lattice mismatched with respect to said fourth subcell, wherein the upper subcell is composed of an AlGaInP emitter layer (206a,206b) and a AlGaInP base layer, the second subcell is composed of AlGaAs emitter layer and a AlGaAs base layer, the third subcell is composed of a GaInP emitter layer and a GaAs base layer, the fourth subcell is composed of a GaInAs emitter layer and a GaInAs base layer, and the bottom fifth subcell is composed of a GaInAs emitter layer and a GaInAs base layer. an upper first solar subcell (206a,206b,206c,207) having a first band gap, and the base-emitter junction (207,206b) of the upper first solar subcell being a homojunction; a second solar subcell (211,212) adjacent to said first solar subcell and having a second band gap smaller than said first band gap; a third solar subcell (216,217) adjacent to said second solar subcell and having a third band gap in a range of approximately 1.3 to 1.5 eV and smaller than said second band gap; a first graded interlayer adjacent to said third solar subcell; said first graded interlayer having a fourth band gap greater than said third band gap; and that is constant at approximately 1.5 eV throughout the thickness of the first graded interlayer; and a fourth solar subcell (224,225) adjacent to said first graded interlayer, said fourth subcell having a fifth band gap of approximately 1.0 to 1.2 eV wherein said fourth subcell is lattice mismatched with respect to said third subcell; a second graded interlayer adjacent to said fourth solar subcell; said second graded interlayer having a sixth band gap greater than said fifth band gap; and that is constant at approximately 1.1 eV throughout the thickness of the second graded interlayer; a lower fifth solar subcell (232,233) adjacent to said second graded interlayer, said lower fifth subcell having a seventh band gap smaller than said fifth band gap wherein that said fifth subcell is lattice mismatched with respect to said fourth subcell, wherein the upper subcell is composed of an AlGaInP emitter layer (206a,206b) and a AlGaInP base layer, the second subcell is composed of AlGaAs emitter layer and a AlGaAs base layer, the third subcell is composed of a GaInP emitter layer and a GaAs base layer, the fourth subcell is composed of a GaInAs emitter layer and a GaInAs base layer, and the bottom fifth subcell is composed of a GaInAs emitter layer and a GaInAs base layer.