1. The problem is to evaluate the expression $5^{-3}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer. 3. Applying this rule, we rewrite $5^{-3}$ as: $$5^{-3} = \frac{1}{5^3}$$ 4. Calculate $5^3$ by multiplying 5 by itself three times: $$5^3 = 5 \times 5 \times 5 = 125$$ 5. Substitute back: $$5^{-3} = \frac{1}{125}$$ 6. Therefore, the value of $5^{-3}$ is $\frac{1}{125}$.