To solve the equation \( \frac{1}{20} - \left( x - \frac{8}{5} \right) = \frac{1}{20} \), follow these steps:

1. Subtract \(\frac{1}{20}\) from both sides of the equation to isolate the term involving \(x\):
\[
\frac{1}{20} - \left( x - \frac{8}{5} \right) - \frac{1}{20} = \frac{1}{20} - \frac{1}{20}
\]

2. Simplify both sides:
\[
- \left( x - \frac{8}{5} \right) = 0
\]

3. Since the left side is equal to zero, we have:
\[
x - \frac{8}{5} = 0
\]

4. Solve for \(x\) by adding \(\frac{8}{5}\) to both sides:
\[
x = \frac{8}{5}
\]

So, the solution to the equation is:
\[
x = \frac{8}{5}
\]