To evaluate the given expression
[tex]\[ \frac{4(x+5)(x+1)}{(x+3)(x-3)} \][/tex]
for [tex]\( x = 5 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the numerator:
[tex]\[
\text{Numerator} = 4 \cdot (5 + 5) \cdot (5 + 1)
\][/tex]
This simplifies to:
[tex]\[
\text{Numerator} = 4 \cdot 10 \cdot 6 = 240
\][/tex]
2. Substitute [tex]\( x = 5 \)[/tex] into the denominator:
[tex]\[
\text{Denominator} = (5 + 3) \cdot (5 - 3)
\][/tex]
This simplifies to:
[tex]\[
\text{Denominator} = 8 \cdot 2 = 16
\][/tex]
3. Divide the numerator by the denominator:
[tex]\[
\frac{\text{Numerator}}{\text{Denominator}} = \frac{240}{16}
\][/tex]
Simplify this fraction:
[tex]\[
\frac{240}{16} = 15
\][/tex]
Therefore, the value of the expression when [tex]\( x = 5 \)[/tex] is:
[tex]\[ \boxed{15} \][/tex]
So, the correct answer is [tex]\( \boxed{15} \)[/tex].
