1. **State the problem:** Calculate $2^5 - (3^2 - 2^3)$.\n\n2. **Recall the order of operations:** Evaluate exponents first, then parentheses, then subtraction.\n\n3. **Calculate each exponent:**\n$$2^5 = 32$$\n$$3^2 = 9$$\n$$2^3 = 8$$\n\n4. **Evaluate inside the parentheses:**\n$$3^2 - 2^3 = 9 - 8 = 1$$\n\n5. **Substitute back and simplify:**\n$$2^5 - (3^2 - 2^3) = 32 - 1 = 31$$\n\n**Final answer:** $31$