To solve the expression

\[
\frac{11}{15} \cdot \left(-\frac{19}{13}\right) + \frac{11}{15} \cdot \left(\frac{7}{13}\right) + \frac{4}{5},
\]

let's compute each term step by step.

### 1. Calculate the first term:
\[
\frac{11}{15} \cdot \left(-\frac{19}{13}\right) = -\frac{11 \cdot 19}{15 \cdot 13} = -\frac{209}{195}
\]

### 2. Calculate the second term:
\[
\frac{11}{15} \cdot \left(\frac{7}{13}\right) = \frac{11 \cdot 7}{15 \cdot 13} = \frac{77}{195}
\]

### 3. Convert \(\frac{4}{5}\) to have a common denominator:
To add this to the other fractions, we convert \(\frac{4}{5}\) to a fraction with a denominator of 195:
\[
\frac{4}{5} = \frac{4 \cdot 39}{5 \cdot 39} = \frac{156}{195}
\]

### 4. Now combine all terms:
\[
-\frac{209}{195} + \frac{77}{195} + \frac{156}{195}
\]

Combine the numerators:
\[
-209 + 77 + 156 = 24
\]

So, we have:
\[
\frac{24}{195}
\]

### 5. Simplify:
The fraction \(\frac{24}{195}\) can be simplified. Finding the greatest common divisor (GCD) of 24 and 195, which is 3, we can simplify:
\[
\frac{24 \div 3}{195 \div 3} = \frac{8}{65}
\]

Thus, the final result is:
\[
\boxed{\frac{8}{65}}
\]