At what temperature do the Celsius and Fahrenheit scales have the same reading?

The formula to convert Celsius to Fahrenheit is:

$$T_F = \frac{9}{5}T_C + 32$$

Let $T_C = T_F = x$.
Substitute $x$ into the conversion formula:

$$x = \frac{9}{5}x + 32$$

Subtract $\frac{9}{5}x$ from both sides of the equation:

$$x - \frac{9}{5}x = 32$$

Combine the terms with $x$:

$$\frac{5}{5}x - \frac{9}{5}x = 32$$ $$-\frac{4}{5}x = 32$$

Multiply both sides by $-\frac{5}{4}$ to isolate $x$:

$$x = 32 \times \left(-\frac{5}{4}\right)$$ $$x = -8 \times 5$$ $$x = -40$$

The temperature at which the Celsius and Fahrenheit scales record the same reading is $\boxed{-40^\circ}$.