Let's break down the expression step by step:

$(15-4)+3-(12-5 \times 2)+(5 + \frac{16}{4})-5+(10-2^2)$

1. First, solve the parentheses: $(15-4) = 11$ $(12 - 5 \times 2) = 12 - 10 = 2$ $\frac{16}{4} = 4$ $2^2 = 4 \quad \Rightarrow \quad (10 - 4) = 6$

2. Now, rewrite the expression with the simplified values: $11 + 3 - 2 + (5 + 4) - 5 + 6$

3. Simplify further: $11 + 3 = 14$ $14 - 2 = 12$ $5 + 4 = 9$ $12 + 9 = 21$ $21 - 5 = 16$ $16 + 6 = 22$

The final answer is 22.

Would you like further explanation or any additional questions? Here's a list to help:

1. What is the order of operations, and why is it important?
2. How do you handle parentheses in multi-step expressions?
3. How do exponents and multiplication interact in an equation?
4. Can the distributive property be used in similar expressions?
5. How would this change if the numbers were fractions?

Tip: When simplifying expressions, remember to follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).