Answer
$\left( \ln x\right) ^{5}+c$
Work Step by Step
$v=\ln x\Rightarrow dv=\dfrac {1}{x}dx$
$$\int 5\dfrac {\left( \ln x\right) ^{4}}{x}dx=5\int \left( \ln x\right) ^{4}\times \dfrac {1}{x}dx=5\int v^{4}dv=5\times \dfrac {v^{5}}{5}+c=v^{5}+c=\left( \ln x\right) ^{5}+c$$
