If 10 be added to four times a certain number,

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

$\therefore 10+4 x=5 x-5$

$\Rightarrow 10+5=5 x-4 x$

$\Rightarrow 15=x$

$\Rightarrow x=15$ (by transposition)

Therefore, the number is 15 .