The equation is given as
\[ -5 = 4 - \frac{3x}{4 - 3x} \]
To identify the value that makes the equation undefined, we need to find when the denominator \(4 - 3x\) equals zero.
We start by setting the denominator equal to zero:
\[ 4 - 3x = 0 \]
Next, we solve for \(x\):
\[ 3x = 4 \]
\[ x = \frac{4}{3} \]
The equation will be undefined when \(x = \frac{4}{3}\) because that will make the denominator zero.
Thus, the value that makes the equation undefined is
\[ \boxed{\frac{4}{3}} \]
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