The problem asks to simplify the expression $(\frac{x^5}{y})^5$.

1. Problem Description

The problem asks to simplify the expression $(\frac{x^5}{y})^5$.

2. Solution Steps

We need to apply the power of a quotient rule and the power of a power rule.

The power of a quotient rule is $(\frac{a}{b})^n = \frac{a^n}{b^n}$.

The power of a power rule is $(a^m)^n = a^{m \cdot n}$.

Applying the power of a quotient rule to the given expression, we get:

$(\frac{x^5}{y})^5 = \frac{(x^5)^5}{y^5}$

Next, applying the power of a power rule to the numerator, we get:

$(x^5)^5 = x^{5 \cdot 5} = x^{25}$

Substituting this back into the expression, we have:

$\frac{(x^5)^5}{y^5} = \frac{x^{25}}{y^5}$

3. Final Answer

The simplified expression is $\frac{x^{25}}{y^5}$.