Ca5Cr3O13 crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 9-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. In the second Ca site, Ca(2) is bonded in a 6-coordinate geometry to one O(10), one O(6), two equivalent O(7), and two equivalent O(9) atoms. In the third Ca site, Ca(3) is bonded in a 6-coordinate geometry to one O(10), one O(4), two equivalent O(7), and two equivalent O(8) atoms. In the fourth Ca site, Ca(4) is bonded to one O(10), one O(5), two equivalent O(8), and two equivalent O(9) atoms to form distorted CaO6 pentagonal pyramids that share corners with three equivalent Cr(2)O4 tetrahedra and  an edgeedge with one Cr(3)O4 tetrahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a tetrahedral geometry to one O(1), one O(4), and two equivalent O(7) atoms. In the second Cr site, Cr(2) is bonded to one O(2), one O(5), and two equivalent O(8) atoms to form CrO4 tetrahedra that share corners with three equivalent Ca(4)O6 pentagonal pyramids. In the third Cr site, Cr(3) is bonded to one O(3), one O(6), and two equivalent O(9) atoms to form CrO4 tetrahedra that share  an edgeedge with one Ca(4)O6 pentagonal pyramid. There are ten inequivalent O sites. In the first O site, O(10) is bonded in a trigonal planar geometry to one Ca(2), one Ca(3), and one Ca(4) atom. In the second O site, O(1) is bonded in a distorted single-bond geometry to two equivalent Ca(1) and one Cr(1) atom. In the third O site, O(2) is bonded in a 3-coordinate geometry to two equivalent Ca(1) and one Cr(2) atom. In the fourth O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ca(1) and one Cr(3) atom. In the fifth O site, O(4) is bonded in a distorted single-bond geometry to one Ca(3), two equivalent Ca(1), and one Cr(1) atom. In the sixth O site, O(5) is bonded in a distorted tetrahedral geometry to one Ca(4), two equivalent Ca(1), and one Cr(2) atom. In the seventh O site, O(6) is bonded in a 4-coordinate geometry to one Ca(2), two equivalent Ca(1), and one Cr(3) atom. In the eighth O site, O(7) is bonded in a 1-coordinate geometry to one Ca(1), one Ca(2), one Ca(3), and one Cr(1) atom. In the ninth O site, O(8) is bonded in a 3-coordinate geometry to one Ca(1), one Ca(3), one Ca(4), and one Cr(2) atom. In the tenth O site, O(9) is bonded in a 4-coordinate geometry to one Ca(1), one Ca(2), one Ca(4), and one Cr(3) atom.
Ca5Cr3O13 crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 9-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. The Ca(1)-O(1) bond length is 2.49 Å. The Ca(1)-O(2) bond length is 2.35 Å. The Ca(1)-O(3) bond length is 2.38 Å. The Ca(1)-O(4) bond length is 2.56 Å. The Ca(1)-O(5) bond length is 2.39 Å. The Ca(1)-O(6) bond length is 2.44 Å. The Ca(1)-O(7) bond length is 3.05 Å. The Ca(1)-O(8) bond length is 2.98 Å. The Ca(1)-O(9) bond length is 2.75 Å. In the second Ca site, Ca(2) is bonded in a 6-coordinate geometry to one O(10), one O(6), two equivalent O(7), and two equivalent O(9) atoms. The Ca(2)-O(10) bond length is 2.19 Å. The Ca(2)-O(6) bond length is 2.61 Å. Both Ca(2)-O(7) bond lengths are 2.59 Å. Both Ca(2)-O(9) bond lengths are 2.39 Å. In the third Ca site, Ca(3) is bonded in a 6-coordinate geometry to one O(10), one O(4), two equivalent O(7), and two equivalent O(8) atoms. The Ca(3)-O(10) bond length is 2.16 Å. The Ca(3)-O(4) bond length is 2.75 Å. Both Ca(3)-O(7) bond lengths are 2.50 Å. Both Ca(3)-O(8) bond lengths are 2.44 Å. In the fourth Ca site, Ca(4) is bonded to one O(10), one O(5), two equivalent O(8), and two equivalent O(9) atoms to form distorted CaO6 pentagonal pyramids that share corners with three equivalent Cr(2)O4 tetrahedra and  an edgeedge with one Cr(3)O4 tetrahedra. The Ca(4)-O(10) bond length is 2.21 Å. The Ca(4)-O(5) bond length is 2.55 Å. Both Ca(4)-O(8) bond lengths are 2.43 Å. Both Ca(4)-O(9) bond lengths are 2.48 Å. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a tetrahedral geometry to one O(1), one O(4), and two equivalent O(7) atoms. The Cr(1)-O(1) bond length is 1.66 Å. The Cr(1)-O(4) bond length is 1.68 Å. Both Cr(1)-O(7) bond lengths are 1.66 Å. In the second Cr site, Cr(2) is bonded to one O(2), one O(5), and two equivalent O(8) atoms to form CrO4 tetrahedra that share corners with three equivalent Ca(4)O6 pentagonal pyramids. The Cr(2)-O(2) bond length is 1.72 Å. The Cr(2)-O(5) bond length is 1.73 Å. Both Cr(2)-O(8) bond lengths are 1.73 Å. In the third Cr site, Cr(3) is bonded to one O(3), one O(6), and two equivalent O(9) atoms to form CrO4 tetrahedra that share  an edgeedge with one Ca(4)O6 pentagonal pyramid. The Cr(3)-O(3) bond length is 1.71 Å. The Cr(3)-O(6) bond length is 1.74 Å. Both Cr(3)-O(9) bond lengths are 1.72 Å. There are ten inequivalent O sites. In the first O site, O(10) is bonded in a trigonal planar geometry to one Ca(2), one Ca(3), and one Ca(4) atom. In the second O site, O(1) is bonded in a distorted single-bond geometry to two equivalent Ca(1) and one Cr(1) atom. In the third O site, O(2) is bonded in a 3-coordinate geometry to two equivalent Ca(1) and one Cr(2) atom. In the fourth O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ca(1) and one Cr(3) atom. In the fifth O site, O(4) is bonded in a distorted single-bond geometry to one Ca(3), two equivalent Ca(1), and one Cr(1) atom. In the sixth O site, O(5) is bonded in a distorted tetrahedral geometry to one Ca(4), two equivalent Ca(1), and one Cr(2) atom. In the seventh O site, O(6) is bonded in a 4-coordinate geometry to one Ca(2), two equivalent Ca(1), and one Cr(3) atom. In the eighth O site, O(7) is bonded in a 1-coordinate geometry to one Ca(1), one Ca(2), one Ca(3), and one Cr(1) atom. In the ninth O site, O(8) is bonded in a 3-coordinate geometry to one Ca(1), one Ca(3), one Ca(4), and one Cr(2) atom. In the tenth O site, O(9) is bonded in a 4-coordinate geometry to one Ca(1), one Ca(2), one Ca(4), and one Cr(3) atom.