1. The problem is to evaluate the expression $2^{-5}$.\n\n2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer.\n\n3. Applying this rule, we rewrite $2^{-5}$ as $$2^{-5} = \frac{1}{2^5}.$$\n\n4. Next, calculate $2^5$: $$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32.$$\n\n5. Substitute back: $$2^{-5} = \frac{1}{32}.$$\n\n6. Therefore, the value of $2^{-5}$ is $\frac{1}{32}$, which is a small positive fraction.