Answer
Yes (when the temperature is $-40^\circ$)
Work Step by Step
We use the formula:
$F=\frac{9}{5}C+32$
Set $F=C$:
$F=\frac{9}{5}F+32$
$\frac{4}{5}F=-32$
$F=-40$
So the temperatures are equal when the temperature is $-40^\circ$.