The integral of $\dfrac{x}5$ is $\boxed{\dfrac{x^2}{10} + C}$.
To find $\displaystyle \int \dfrac{x}5 \: dx$, we may pull out the constant $\dfrac15$. After doing so, we end up having to find the integral of $x$ using the power rule:
\[\begin{align*} \int x^n \: dx &= \dfrac{x^{n + 1}}{n + 1} + C \end{align*}\]
Plugging in our function $f(x) = \dfrac{x}5$:
\[\begin{align*} \int \dfrac{x}5 \: dx &= \dfrac15 \int x \: dx\\ &= \dfrac15 \cdot \dfrac{x^2}2 + C\\\ &= \dfrac{x^2}{10} + C \end{align*}\]
We get that $\displaystyle \int \dfrac{x}5 \: dx = \boxed{\dfrac{x^2}{10} + C}$.
Reminder that as this is an indefinite integral, we must include the $+ C$ after the calculation of the integral. It is a common mistake to leave out the constant term.
