To evaluate the function \( f(x) = 4^x + 5 \) at \( x = 2 \), we substitute \( 2 \) into the function:
\[ f(2) = 4^2 + 5 \]
Now, calculate \( 4^2 \):
\[ 4^2 = 16 \]
Now, add \( 5 \):
\[ f(2) = 16 + 5 = 21 \]
Thus, the value of \( f(2) \) is \( 21 \).