To solve the expression $10 - 3 \times (5 - 2)$, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right)).

1. First, simplify inside the parentheses: $5 - 2 = 3$ So the expression becomes: $10 - 3 \times 3$

2. Next, perform the multiplication: $3 \times 3 = 9$ Now the expression is: $10 - 9$

3. Finally, subtract: $10 - 9 = 1$

Thus, the result is $\boxed{1}$.

Would you like more details on this process or have any questions?

Here are some related questions:

1. How do we apply the order of operations to more complex equations?
2. What happens if there are exponents in such expressions?
3. How can we solve equations with multiple parentheses?
4. How does the order change when both multiplication and division are involved?
5. Can negative numbers change the outcome when subtracting from an expression?

Tip: Always handle the operations inside parentheses first before moving to multiplication or subtraction.