Step 1: Calculate the semi-perimeter (s)

The semi-perimeter $s$ of the triangle is given by half of the sum of all sides: $s = \frac{a + b + c}{2}$

$s = \frac{5 + 7 + 10}{2} = \frac{22}{2} = 11\text{ cm}$

Step 2: Apply Heron's Formula

Substitute $s = 11$, $a = 5$, $b = 7$, and $c = 10$ into Heron's area formula: $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$

$\text{Area} = \sqrt{11(11-5)(11-7)(11-10)}$

Step 3: Simplify the terms inside the square root

Evaluate the differences: $(11-5) = 6$, $(11-7) = 4$, and $(11-10) = 1$. Multiply these values together: $11 \times 6 \times 4 \times 1 = 264$.

$\text{Area} = \sqrt{11 \times 6 \times 4 \times 1} = \sqrt{264}$

Step 4: Simplify the radical

Factor out the perfect square from $264$: $264 = 4 \times 66$, so $\sqrt{264} = \sqrt{4 \times 66} = 2\sqrt{66}$.

$\text{Area} = 2\sqrt{66}\text{ cm}^2$