Answer :

To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \cdot 3^x \)[/tex], follow these steps:

1. Start with the given function:
[tex]\[
f(x) = \frac{1}{9} \cdot 3^x
\][/tex]

2. Substitute [tex]\( x \)[/tex] with 5:
[tex]\[
f(5) = \frac{1}{9} \cdot 3^5
\][/tex]

3. Calculate [tex]\( 3^5 \)[/tex]:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]

4. Substitute [tex]\( 3^5 \)[/tex] back into the function:
[tex]\[
f(5) = \frac{1}{9} \cdot 243
\][/tex]

5. Simplify the multiplication:
[tex]\[
f(5) = \frac{243}{9}
\][/tex]

6. Perform the division:
[tex]\[
\frac{243}{9} = 27
\][/tex]

Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].

So, the correct answer is:
C. 27