As shown in the figure, a given line segment AB is divided into 2:3 segments by point m, and 4:1 segments by point n. if Mn is equal to 5cm, then the line segment BN=________ .

AB is divided into 2:3 segments by point m: BM is 3 △ (2 + 3) = 3 / 5 of AB length; ab is divided into 4:1 segments by point n: BN is 1 △ (4 + 1) = 1 / 5 of AB length; BN is 3 / 5-1 / 5 = 2 / 5 of AB length; if Mn = 5 cm, then AB is 5 △ (4 / 5-2 / 5) = 12.5 cm, then BN is 12.5

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