To determine which value is equivalent to the expression [tex]\( x^2 - 3x + 2 \)[/tex] when [tex]\( x = 5 \)[/tex], we follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the expression:
[tex]\[
x^2 - 3x + 2 \implies 5^2 - 3(5) + 2
\][/tex]
2. Calculate [tex]\( 5^2 \)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
3. Calculate [tex]\( 3(5) \)[/tex]:
[tex]\[
3 \cdot 5 = 15
\][/tex]
4. Substitute these calculated values back into the expression:
[tex]\[
25 - 15 + 2
\][/tex]
5. Perform the addition and subtraction in order:
[tex]\[
25 - 15 = 10
\][/tex]
[tex]\[
10 + 2 = 12
\][/tex]
Thus, when [tex]\( x = 5 \)[/tex], the expression [tex]\( x^2 - 3x + 2 \)[/tex] evaluates to 12.
Therefore, the correct answer is:
[tex]\[
\boxed{12}
\][/tex]
So, the corresponding answer in the given options is:
[tex]\[
\boxed{C}
\][/tex]
