To solve the equation \(5(19 - x) - 38 = 32\), follow these steps:

1. Distribute the 5 inside the parentheses:
\[
5 \cdot 19 - 5 \cdot x - 38 = 32
\]
This simplifies to:
\[
95 - 5x - 38 = 32
\]

2. Combine the constant terms on the left side:
\[
95 - 38 - 5x = 32
\]
Simplifying further:
\[
57 - 5x = 32
\]

3. Isolate the term with \(x\) by subtracting 57 from both sides:
\[
57 - 5x - 57 = 32 - 57
\]
This simplifies to:
\[
-5x = -25
\]

4. Solve for \(x\) by dividing both sides by -5:
\[
x = \frac{-25}{-5}
\]
Simplifying this gives:
\[
x = 5
\]

So, the solution to the equation \(5(19 - x) - 38 = 32\) is \(x = 5\).