To evaluate the expression $x^2 - 3y + 12$ given $x = -2$ and $y = 5$:

1. Substitute $x = -2$ and $y = 5$ into the expression: $(-2)^2 - 3(5) + 12$

2. Calculate $(-2)^2$: $(-2)^2 = 4$

3. Calculate $-3(5)$: $-3(5) = -15$

4. Substitute the values back into the expression: $4 - 15 + 12$

5. Perform the addition and subtraction: $4 - 15 = -11$ $-11 + 12 = 1$

So, the value of the expression is $1$.

Would you like further details or have any questions? Here are five related questions:

1. What would the expression evaluate to if $x = 3$ and $y = 4$?
2. How does the expression change if the coefficient of $y$ is doubled?
3. What is the general form of the expression when expanded?
4. Can you find the roots of the expression $x^2 - 3y + 12 = 0$ for given $y$ values?
5. How does changing the constant term (12) affect the outcome?

Tip: When evaluating expressions, always perform operations in the correct order: exponents first, then multiplication/division, and finally addition/subtraction.