Find the number whose fifth part increased by 5

Let the number be $\mathrm{x}$.

Fifth part increased by $5=\frac{\mathrm{x}}{5}+5$

Fourt part diminished by $5=\frac{x}{4}-5$

$\therefore \frac{x}{5}+5=\frac{x}{4}-5$

$\Rightarrow 5+5=\frac{x}{4}-\frac{x}{5}$

$\Rightarrow 10=\frac{5 x-4 x}{20}$

$\Rightarrow 10=\frac{x}{20}$

$\Rightarrow 200=x$

$\Rightarrow x=200$

Therefore, the number is 200 .