Answer
Diverges
Work Step by Step
\begin{aligned}
\int_{0}^{5} \frac{d x}{x^{20 / 19}} &=\lim _{R \rightarrow 0} \int_{R}^{5} \frac{d x}{x^{20 / 19}} \\
&=\lim _{R \rightarrow 0} \left(\frac{x^{(-1 / 19)}}{-1 / 19}\right)\bigg|_{R} ^{5} \\ &=\lim _{R \rightarrow 0}\left( \frac{-19}{5^{(1 / 19)}}+\frac{19}{R^{(1 / 19)}} \right)\\ &=\infty \end{aligned}
Then the integral diverges.
