#### Answer

$\frac{1}{25}$

#### Work Step by Step

To multiply powers with the same base, we add the exponents. The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$ We use these rules to rewrite the expression and simplify: $$5^{-3}\cdot 5=5^{-2}=\frac{1}{5^2}=\frac{1}{25}$$