To evaluate the expression $3(x - 4) + 2x - x^2$ for $x = 5$, follow these steps:

1. Substitute $x = 5$ into the expression:

   $3(5 - 4) + 2(5) - 5^2$

2. Simplify inside the parentheses:

   $3(1) + 2(5) - 5^2$

3. Multiply and square the values:

   $3 \times 1 + 2 \times 5 - 25$

   $3 + 10 - 25$

4. Add and subtract the results:

   $13 - 25 = -12$

So, the value of the expression when $x = 5$ is $\boxed{-12}$.

Would you like more details or have any questions about this solution?

Here are five related questions to expand your understanding:

1. What happens if you evaluate the same expression for $x = -5$?
2. How would the expression change if the $x^2$ term had a positive coefficient?
3. What is the significance of the order of operations in this expression?
4. How does the value of the expression change as $x$ increases or decreases?
5. Can you factor the expression before substituting the value of $x$?

Tip: Always perform operations inside parentheses first before moving on to multiplication, division, addition, and subtraction.