Let's solve the expression step-by-step.

The expression is:

\[
2^7 \div 2^2 + 5^4 \cdot 2^4 - 3 \cdot 2^5
\]

### Step 1: Simplify \( 2^7 \div 2^2 \)

Using the quotient rule for exponents:

\[
2^7 \div 2^2 = 2^{7-2} = 2^5
\]

Calculating \( 2^5 \):

\[
2^5 = 32
\]

### Step 2: Calculate \( 5^4 \cdot 2^4 \)

First, we compute \( 5^4 \):

\[
5^4 = 625
\]

Now calculate \( 2^4 \):

\[
2^4 = 16
\]

Now multiply \( 625 \) and \( 16 \):

\[
5^4 \cdot 2^4 = 625 \cdot 16 = 10000
\]

### Step 3: Calculate \( 3 \cdot 2^5 \)

We already know \( 2^5 = 32 \):

\[
3 \cdot 2^5 = 3 \cdot 32 = 96
\]

### Step 4: Combine all parts

Now we combine everything:

\[
2^7 \div 2^2 + 5^4 \cdot 2^4 - 3 \cdot 2^5 = 32 + 10000 - 96
\]

Calculate \( 32 + 10000 \):

\[
32 + 10000 = 10032
\]

Now subtract \( 96 \):

\[
10032 - 96 = 9986
\]

### Final Result

The final result of the expression is:

\[
\boxed{9986}
\]