Answer :

GinnyAnswer
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].

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