Let's solve the expression step by step:

1. Evaluate the exponentiation: $-\left(3\right)^{2} = -(3 \times 3) = -9$

2. Multiply: $5 \cdot 2 = 10$

3. Add the results: $-9 + 10 = 1$

So, the value of the expression $-\left(3\right)^{2} + 5 \cdot 2$ is 1.

Would you like more details or have any questions? Here are some related problems:

1. Simplify $-\left(4\right)^{2} + 6 \cdot 3$.
2. What is the value of $-\left(2\right)^{3} + 4 \cdot 3$?
3. Evaluate $-\left(5\right)^{2} + 7 \cdot 2$.
4. Solve $-\left(6\right)^{2} + 8 \cdot 2$.
5. What is $-\left(7\right)^{2} + 9 \cdot 2$?

Tip: Always follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and then addition and subtraction (from left to right).