1. The problem asks to perform the operation and simplify the expression $(5i)^2$ where $i$ is the imaginary unit. 2. Recall that $i$ is defined as $i^2 = -1$. 3. Use the property of exponents: $(ab)^2 = a^2 b^2$. Here, $a=5$ and $b=i$. 4. Calculate: $$ (5i)^2 = 5^2 \times i^2 = 25 \times (-1) = -25 $$ 5. Therefore, the simplified form of $(5i)^2$ is $-25$. This is a purely real number since the imaginary unit squared is $-1$.