Use Simpson's rule to estimate the error of integral $\int_1^5 \ln(x) \mathrm dx$

Question

In my homework I'm requested to estimate the error of the definite integral:

1. $$\int_1^5 \ln(x) \mathrm dx$$

I am also given the formula:

2. $$|E_n|<= \frac {(K(b-a)^5)}{180N^4}$$

Where K is an upper bound for the fourth derivative ($|f^4(x)|$). Given that $$|f^4(\ln (x))| = -\frac {6}{x^4}$$

I have to assume that $$|f^4(\ln (x))| = -\frac {6}{x^4} = -\frac {6}{5^4} = 0.0096$$

If I plug this value into the formula (2) I get [$2.133*10^{-4}$] which I am not sure about.

Any further explanation will be appreciated. I use Thomas Calculus and can't find much more.

Thanks