#### Answer

n has values of 1 and -1.

#### Work Step by Step

To solve for value of n, we will simplify the equation $n^{-3}$ = $(\frac{1}{5})^{5}$.
so $n^{-3}$. = $\frac{1}{n^{3}}$ and $(\frac{1}{5})^{5}$ = $\frac{1}{n^{5}}$
$\frac{1}{n^{3}}$ = $\frac{1}{n^{5}}$. --> Cross Multiply
$\frac{n^{5}}{n^{3}}$ = 1
$n^{5-3}$ = 1
$n^{2}$ = 1
n = $\sqrt 1$
n = -1,1
Therefore the values of n are 1 and -1.