The problem states that $f(1) = 5$ and gives a recursive relation for $f(n)$ as follows:

$f(n) = 5 f(n - 1)$

We are asked to find the value of $f(6)$.

Step-by-Step Solution

Using the given information and the recursive formula, let's find the values of $f(2)$, $f(3)$, $f(4)$, $f(5)$, and $f(6)$.

1. Given: $f(1) = 5$.
2. Find $f(2)$: $f(2) = 5 \cdot f(1) = 5 \cdot 5 = 25$
3. Find $f(3)$: $f(3) = 5 \cdot f(2) = 5 \cdot 25 = 125$
4. Find $f(4)$: $f(4) = 5 \cdot f(3) = 5 \cdot 125 = 625$