To determine the value that makes the equation \( -5 = \frac{4 - 3x}{4 - 3x} \) undefined, we need to identify when the denominator of the fraction is equal to zero, because a fraction is undefined when its denominator is zero.
The given expression has the same expression in both the numerator and denominator, which is \( 4 - 3x \). Thus, the fraction is undefined when:
\[ 4 - 3x = 0 \]
Now, we solve for \( x \):
\[ 4 = 3x \]
Dividing both sides by 3 gives:
\[ x = \frac{4}{3} \]
Therefore, the equation becomes undefined when \( x = \frac{4}{3} \).