Answer
$-\displaystyle \frac{1}{20}$
Work Step by Step
$\displaystyle \left(\frac{-1}{4} \right)=\left(-\frac{1}{4} \right) \qquad $ equivalent signed fractions.
$\displaystyle \left(\frac{1}{-5} \right)=\left(-\frac{1}{5} \right) \qquad $ equivalent signed fractions.
Subtracting the signed numbers, change the sign of the number being subtracted and add:
$ \begin{array}{lll}
(-\dfrac{1}{4} )-(-\dfrac{1}{5} ) & =(-\dfrac{1}{4} )+(+\dfrac{1}{5} ) & \text{LCD=20} \\
& =(\dfrac{-5}{20} )+(\dfrac{4}{20} ) & \text{combine numerators} & & \\
& =\dfrac{-5+4}{20} & \text{apply addition of}\\
& =\dfrac{-1}{20} & \text{two numbers with unlike signs}\\
& = -\dfrac{1}{20} & \\
& &
\end{array}$
