1. **State the problem:** Simplify the expression $-2^{2}+4[16-:(3-5)]$. 2. **Understand the order of operations:** We follow PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)). 3. **Evaluate exponents:** $-2^{2}$ means $-(2^{2}) = -4$ because exponentiation comes before the negative sign. 4. **Simplify inside the brackets:** The expression inside the brackets is $16-:(3-5)$. The symbol $-:$ is interpreted as subtraction and division. First, calculate the parentheses: $$3-5 = -2$$ 5. **Rewrite the bracket expression:** $16 - : (-2)$ means $16 - \frac{1}{-2}$ or $16 - (-\frac{1}{2})$ if $-:$ is division after subtraction. However, since the symbol is ambiguous, we interpret $-:$ as division, so $16 - : (-2)$ means $16 \div (-2)$. 6. **Calculate division:** $$16 \div (-2) = -8$$ 7. **Multiply by 4:** $$4 \times (-8) = -32$$ 8. **Combine all parts:** $$-4 + (-32) = -36$$ **Final answer:** $$\boxed{-36}$$