To solve the expression \(-\frac{5}{7} \cdot \frac{2}{11} + \frac{5}{7} \cdot \frac{9}{11}\), follow these steps:

1. **Multiply the fractions:**
- For the first term: \(-\frac{5}{7} \cdot \frac{2}{11} = -\frac{5 \cdot 2}{7 \cdot 11} = -\frac{10}{77}\)
- For the second term: \(\frac{5}{7} \cdot \frac{9}{11} = \frac{5 \cdot 9}{7 \cdot 11} = \frac{45}{77}\)

2. **Add the results:**
- \(-\frac{10}{77} + \frac{45}{77}\)

Since the denominators are the same, you can combine the numerators directly:

\[
-\frac{10}{77} + \frac{45}{77} = \frac{-10 + 45}{77} = \frac{35}{77}
\]

3. **Simplify the fraction:**
- The greatest common divisor (GCD) of 35 and 77 is 7.
- Divide both the numerator and the denominator by 7:

\[
\frac{35}{77} = \frac{35 \div 7}{77 \div 7} = \frac{5}{11}
\]

So, the simplified result of the expression \(-\frac{5}{7} \cdot \frac{2}{11} + \frac{5}{7} \cdot \frac{9}{11}\) is \(\frac{5}{11}\).