Step 1: Think in terms of woman-years. The total observation is 100 women followed for 24 months, that is $\dfrac{100 \times 24}{12} = 200$ woman-years of contraceptive use. Step 2: The Pearl Index is simply pregnancies divided by woman-years, scaled to 100 woman-years: $\text{PI} = \dfrac{\text{pregnancies}}{\text{woman-years}} \times 100$. Step 3: Plug in 10 pregnancies over 200 woman-years: $\text{PI} = \dfrac{10}{200} \times 100 = 5$. Step 4: This matches the standard formula result, confirming a Pearl Index of 5 failures per 100 woman-years. \[\boxed{5}\]