We are given a geometric sequence $\{a_n\}$. We know that $a_4 = 5$. We need to find the value of $a_3 \cdot a_5$.

1. Problem Description

We are given a geometric sequence $\{a_n\}$. We know that $a_4 = 5$. We need to find the value of $a_3 \cdot a_5$.

2. Solution Steps

Since $\{a_n\}$ is a geometric sequence, we have $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio.

We are given that $a_4 = 5$. We can express $a_4$ as $a_4 = a_1 \cdot r^{4-1} = a_1 \cdot r^3 = 5$.

We want to find $a_3 \cdot a_5$. We can write $a_3 = a_1 \cdot r^{3-1} = a_1 \cdot r^2$ and $a_5 = a_1 \cdot r^{5-1} = a_1 \cdot r^4$.

Therefore, $a_3 \cdot a_5 = (a_1 \cdot r^2) \cdot (a_1 \cdot r^4) = a_1^2 \cdot r^6 = (a_1 \cdot r^3)^2$.

Since $a_1 \cdot r^3 = a_4 = 5$, we have $a_3 \cdot a_5 = (a_4)^2 = 5^2 = 25$.

3. Final Answer

25