1. **State the problem:** Evaluate the expression $$\frac{2^3 + 5(5 - 4)}{17 - 2 \cdot 2}$$. 2. **Recall the order of operations:** We first evaluate exponents, then parentheses, multiplication and division from left to right, and finally addition and subtraction. 3. **Evaluate the numerator:** - Calculate the exponent: $$2^3 = 8$$. - Calculate inside the parentheses: $$5 - 4 = 1$$. - Multiply: $$5 \times 1 = 5$$. - Add: $$8 + 5 = 13$$. 4. **Evaluate the denominator:** - Multiply: $$2 \cdot 2 = 4$$. - Subtract: $$17 - 4 = 13$$. 5. **Form the fraction:** $$\frac{13}{13}$$. 6. **Simplify the fraction:** - Cancel common factors: $$\frac{\cancel{13}}{\cancel{13}} = 1$$. 7. **Final answer:** $$1$$.