To simplify the expression \( 5^9 \cdot 5^{-13} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this to the expression:
\[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{9 - 13} = 5^{-4} \]
Now, \( 5^{-4} \) can be rewritten as:
\[ 5^{-4} = \frac{1}{5^4} \]
Calculating \( 5^4 \):
\[ 5^4 = 5 \times 5 \times 5 \times 5 = 625 \]
Therefore,
\[ 5^{-4} = \frac{1}{625} \]
So, the simplified expression is:
\[ \frac{1}{625} \]