To solve the equation \(-\frac{5}{7}\left(\frac{2}{5} - x\right) - \frac{1}{3} = \frac{1}{4} - \frac{3}{10}\), let's follow these steps:

1. Simplify the right-hand side of the equation.
2. Distribute and simplify the left-hand side.
3. Combine like terms and solve for \(x\).

### Step 1: Simplify the right-hand side

First, find a common denominator for \(\frac{1}{4}\) and \(\frac{3}{10}\). The least common multiple of 4 and 10 is 20.

\[
\frac{1}{4} = \frac{5}{20}
\]
\[
\frac{3}{10} = \frac{6}{20}
\]

Now subtract the fractions:

\[
\frac{5}{20} - \frac{6}{20} = \frac{5 - 6}{20} = -\frac{1}{20}
\]

So the equation becomes:

\[
-\frac{5}{7}\left(\frac{2}{5} - x\right) - \frac{1}{3} = -\frac{1}{20}
\]

### Step 2: Distribute and simplify the left-hand side

Distribute \(-\frac{5}{7}\) inside the parentheses:

\[
-\frac{5}{7} \cdot \frac{2}{5} + \frac{5}{7}x = -\frac{10}{35} + \frac{5}{7}x = -\frac{2}{7} + \frac{5}{7}x
\]

So the equation now is:

\[
-\frac{2}{7} + \frac{5}{7}x - \frac{1}{3} = -\frac{1}{20}
\]

### Step 3: Combine like terms and solve for \(x\)

First, let's combine the constants on the left-hand side. To do this, find a common denominator for \(\frac{2}{7}\) and \(\frac{1}{3}\). The least common multiple of 7 and 3 is 21.

\[
-\frac{2}{7} = -\frac{6}{21}
\]
\[
-\frac{1}{3} = -\frac{7}{21}
\]

Combine these:

\[
-\frac{6}{21} - \frac{7}{21} = -\frac{13}{21}
\]

So the equation now is:

\[
-\frac{13}{21} + \frac{5}{7}x = -\frac{1}{20}
\]

Next, isolate \(\frac{5}{7}x\):

\[
\frac{5}{7}x = -\frac{1}{20} + \frac{13}{21}
\]

Find a common denominator for \(-\frac{1}{20}\) and \(\frac{13}{21}\). The least common multiple of 20 and 21 is 420.

\[
-\frac{1}{20} = -\frac{21}{420}
\]
\[
\frac{13}{21} = \frac{260}{420}
\]

Combine these:

\[
-\frac{21}{420} + \frac{260}{420} = \frac{239}{420}
\]

So the equation now is:

\[
\frac{5}{7}x = \frac{239}{420}
\]

Solve for \(x\) by multiplying both sides by \(\frac{7}{5}\):

\[
x = \frac{239}{420} \cdot \frac{7}{5} = \frac{239 \cdot 7}{420 \cdot 5} = \frac{1673}{2100}
\]

So the solution is:

\[
x = \frac{1673}{2100}
\]