We start with the expression \( 5 + 8 \cdot 2^{3} - 3 \cdot 2 \). According to the order of operations, we first calculate the exponentiation:
\[ 2^{3} = 8 \]
Substituting this back into the expression gives us:
\[ 5 + 8 \cdot 8 - 3 \cdot 2 \]
Next, we perform the multiplications:
\[ 8 \cdot 8 = 64 \quad \text{and} \quad 3 \cdot 2 = 6 \]
Now, substituting these values back into the expression results in:
\[ 5 + 64 - 6 \]
Finally, we perform the addition and subtraction:
\[ 5 + 64 = 69 \] \[ 69 - 6 = 63 \]
The original equation \( 5 + 8 \cdot 2^{3} - 3 \cdot 2 = 63 \) holds true, thus confirming that:
\[ \boxed{63} \]
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