Write the following set in the set-builder form: $\{ 5, 25, 125, 625 \}$

(N/A) The given set is $A = \{ 5, 25, 125, 625 \}$.
Observe the elements of the set:
$5 = 5^{1}$
$25 = 5^{2}$
$125 = 5^{3}$
$625 = 5^{4}$
It can be seen that each element is of the form $5^{n}$,where $n$ is a natural number such that $1 \le n \le 4$.
Therefore,the set-builder form is $\{ x : x = 5^{n}, n \in N \text{ and } 1 \le n \le 4 \}$.