To simplify the expression \( \frac{2^{18} - 2^3}{2^{20} - 2^5} \), we will start by factoring out common terms in both the numerator and the denominator.

### Step 1: Factor the numerator

The numerator is:

\[
2^{18} - 2^3 = 2^3(2^{15} - 1)
\]

### Step 2: Factor the denominator

The denominator is:

\[
2^{20} - 2^5 = 2^5(2^{15} - 1)
\]

### Step 3: Substitute the factored forms into the expression

Now substituting these factored forms into the original expression:

\[
\frac{2^{18} - 2^3}{2^{20} - 2^5} = \frac{2^3(2^{15} - 1)}{2^5(2^{15} - 1)}
\]

### Step 4: Cancel the common factors

Both the numerator and denominator share the factor \( 2^{15} - 1 \). Assuming \( 2^{15} - 1 \neq 0 \), we can cancel this factor out:

\[
= \frac{2^3}{2^5}
\]

### Step 5: Simplify the fraction

Now, we simplify \( \frac{2^3}{2^5} \):

\[
= 2^{3 - 5} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4}
\]

### Final Result

Thus, the simplified result of the expression \( \frac{2^{18} - 2^3}{2^{20} - 2^5} \) is:

\[
\boxed{\frac{1}{4}}
\]