To find the amount of money in the bank at the end of 5 years using the formula \( f(x) = 4000(1.06)^x \), we will substitute \( x = 5 \) into the formula.
\[ f(5) = 4000(1.06)^5 \]
Now, we need to calculate \( (1.06)^5 \):
\[ (1.06)^5 \approx 1.338225 \]
Next, we multiply this by 4000:
\[ f(5) = 4000 \times 1.338225 \approx 5352.90 \]
Thus, the amount of money in the bank at the end of 5 years is approximately:
\[ f(5) \approx 5352.90 \]
Therefore, rounding to the nearest cent,
\[ f(5) = \boxed{5352.90} \]