The height of an equilateral triangle is $5\sqrt{3}$ cm, then its area is:

For an equilateral triangle with side length $a$:

Height: $h = \frac{\sqrt{3}}{2} \times a$

Area: $Area = \frac{\sqrt{3}}{4} \times a^2$

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Given height $h = 5\sqrt{3}$ cm.

Using the height formula:

$5\sqrt{3} = \frac{\sqrt{3}}{2} \times a$

$a = \frac{5\sqrt{3} \times 2}{\sqrt{3}}$

$a = \frac{10\sqrt{3}}{\sqrt{3}}$

$a = 10$ cm

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Using the area formula with $a = 10$ cm:

$Area = \frac{\sqrt{3}}{4} \times a^2$

$Area = \frac{\sqrt{3}}{4} \times (10)^2$

$Area = \frac{\sqrt{3}}{4} \times 100$

$Area = 25\sqrt{3}$ cm²

Therefore, the area of the equilateral triangle is $25\sqrt{3}$ cm².