The problem asks to simplify the expression $\sqrt{75x^2y^5}$.

1. Problem Description

The problem asks to simplify the expression $\sqrt{75x^2y^5}$.

2. Solution Steps

First, we can rewrite 75 as $25 \times 3$. Thus, the expression becomes:

$\sqrt{25 \times 3 \times x^2 \times y^5}$

We can also rewrite $y^5$ as $y^4 \times y$. Thus, the expression becomes:

$\sqrt{25 \times 3 \times x^2 \times y^4 \times y}$

Now, we can separate the square root into multiple square roots:

$\sqrt{25} \times \sqrt{3} \times \sqrt{x^2} \times \sqrt{y^4} \times \sqrt{y}$

We know that:

$\sqrt{25} = 5$

$\sqrt{x^2} = |x|$

$\sqrt{y^4} = y^2$

Substituting these values, we get:

$5 \times \sqrt{3} \times |x| \times y^2 \times \sqrt{y}$

Combining the terms, we get:

$5|x|y^2\sqrt{3y}$

3. Final Answer

$5|x|y^2\sqrt{3y}$