jmc

Let $n$ be the desired the number, so adding the number to the numerator and denominator of $\frac{5}{8}$ gives $\frac{5+n}{8+n}$, and we must have $$\frac{5+n}{8+n}=\mathrm{0.4.}$$ Writing $0.4$ as a fraction, we have $$\frac{5+n}{8+n}=\frac{2}{5}.$$Multiplying both sides by $8+n$ and by 5 gives $$5(5+n)=2(8+n).$$Expanding both sides gives$$25+5n=16+2n.$$Subtracting 25 and $2n$ from both sides gives $3n=-9$, so $n=\boxed{-3}.$