A number whose fifth part increased by 5 is equal to its fourth part diminished by 5.

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

According to the question,

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

or $\frac{\mathrm{x}}{5}-\frac{\mathrm{x}}{4}=-5-5$

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

or $-\mathrm{x}=-200[$ After cross multiplication $]$

or $x=200$

Thus, the number is 200 .