What number should be added to

Let the required number be x.

Now,

$\frac{-5}{8}+x=\frac{-3}{2}$

$\Rightarrow \frac{-5}{8}+x+\frac{5}{8}=\frac{-3}{2}+\frac{5}{8} \quad$ (Adding $\frac{5}{8}$ to both the sides)

$\Rightarrow x=\left(\frac{-3}{2}+\frac{5}{8}\right)$

$\Rightarrow x=\left(\frac{-12}{8}+\frac{5}{8}\right)$

$\Rightarrow x=\left(\frac{-12+5}{8}\right)$

$\Rightarrow x=\frac{-7}{8}$

Hence, the required number is $\frac{-7}{8}$.