5. (10 points) As shown in the figure, the area of $\triangle A B C$ is 100 square centimeters, and the area of $\triangle A B D$ is 72 square centimeters. $M$ is the midpoint of side $C D$, $\angle M H B=90^{\circ}$, and it is known that $A B=20$ centimeters. Then the length of $M H$ is $\qquad$ centimeters.
【Analysis】We can use the area formula
Use the median property of $M H$ to find $N$
The area of $\triangle A B D = 72 = \frac{1}{2} \times \mathrm{DE} \times \mathrm{AB} = \frac{1}{2} \times \mathrm{DE} \times 20, \therefore D E = 7.2$ cm, the area of $\triangle A B C = 100 = \frac{1}{2} \times \mathrm{CF} \times \mathrm{AB} = \frac{1}{2} \times \mathrm{CF} \times 20, \therefore C F = 10$ cm; also, $\because M H = \frac{1}{2} \times (\mathrm{DE} + \mathrm{CF}) = \frac{1}{2} \times (7.2 + 10) = 8.6$ cm.

Therefore, the answer is: 8.6.