How did you get 2/5

It seems there might be a misunderstanding, as the fraction $2/5$ does not appear in the solution.

The exponent we calculated was $u^{-1/5 + 1}$.
To add these, we find a common denominator:

$$- \frac{1}{5} + 1 = - \frac{1}{5} + \frac{5}{5} = \frac{-1 + 5}{5} = \frac{4}{5}$$

This resulted in $u^{4/5}$.

Then, when integrating $\int u^{n} \, du = \frac{u^{n+1}}{n+1} + C$, we divided by the new exponent:

$$\frac{u^{4/5}}{4/5}$$

Dividing by a fraction is the same as multiplying by its reciprocal:

$$\frac{u^{4/5}}{4/5} = \frac{5}{4} u^{4/5}$$

This is where the fraction $\frac{4}{5}$ (as an exponent) and its reciprocal $\frac{5}{4}$ (as a coefficient) appear.