To solve for [tex]\( f(5) \)[/tex] given the function [tex]\( f(x) = x^3 - 6x^2 + 6x + 5 \)[/tex], we need to substitute [tex]\( x = 5 \)[/tex] into the function and simplify step by step:
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = 5^3 - 6 \cdot 5^2 + 6 \cdot 5 + 5
\][/tex]
2. Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
3. Calculate [tex]\( 6 \cdot 5^2 \)[/tex]:
[tex]\[
6 \cdot 5^2 = 6 \cdot (5 \cdot 5) = 6 \cdot 25 = 150
\][/tex]
4. Calculate [tex]\( 6 \cdot 5 \)[/tex]:
[tex]\[
6 \cdot 5 = 30
\][/tex]
5. Substitute these values back into the function:
[tex]\[
f(5) = 125 - 150 + 30 + 5
\][/tex]
6. Simplify the expression by performing the addition and subtraction in order:
[tex]\[
125 - 150 = -25
\][/tex]
[tex]\[
-25 + 30 = 5
\][/tex]
[tex]\[
5 + 5 = 10
\][/tex]
Therefore, [tex]\( f(5) = 10 \)[/tex].
