Let's solve the equation step by step.

The given equation is:

\[ 2x - 5 = \frac{4}{32}x - 5 = \frac{4}{3} \]

It seems there might be a bit of confusion since you've written two equalities. Let's denote this as two separate equations.

1. **Equation 1**: \( 2x - 5 = \frac{4}{32}x \)
2. **Equation 2**: \( 2x - 5 = \frac{4}{3} \)

We'll start with **Equation 1**:

\[ 2x - 5 = \frac{4}{32}x \]

First, simplify \(\frac{4}{32}\):

\[ \frac{4}{32} = \frac{1}{8} \]

So the equation becomes:

\[ 2x - 5 = \frac{1}{8}x \]

Now, let's get all terms involving \(x\) on one side:

\[ 2x - \frac{1}{8}x = 5 \]

To combine \(2x\) and \(-\frac{1}{8}x\), we can convert \(2x\) to a fraction with a denominator of 8:

\[ 2x = \frac{16}{8}x \]

Thus,

\[ \frac{16}{8}x - \frac{1}{8}x = 5 \]
\[ \frac{15}{8}x = 5 \]

Now, multiply both sides by \(\frac{8}{15}\) to isolate \(x\):

\[ x = 5 \cdot \frac{8}{15} = \frac{40}{15} = \frac{8}{3} \]

Now let's solve **Equation 2**:

\[ 2x - 5 = \frac{4}{3} \]

Add 5 to both sides:

\[ 2x = \frac{4}{3} + 5 \]

Convert 5 to a fraction with a denominator of 3:

\[ 5 = \frac{15}{3} \]

Now add:

\[ 2x = \frac{4}{3} + \frac{15}{3} = \frac{19}{3} \]

Now, divide both sides by 2:

\[ x = \frac{19}{3} \cdot \frac{1}{2} = \frac{19}{6} \]

So the solutions for the equations are:

1. For the first equation: \( x = \frac{8}{3} \)
2. For the second equation: \( x = \frac{19}{6} \)

If you need further assistance or clarification, feel free to ask!