To solve the expression
\[ -\frac{24}{5} + \left(-\frac{25}{2}\right), \]
we first need a common denominator to combine the fractions.
The denominators here are 5 and 2. The least common denominator (LCD) of 5 and 2 is 10.
Now, we will convert each fraction to have the denominator of 10:
- Convert \(-\frac{24}{5}\):
\[ -\frac{24}{5} = -\frac{24 \times 2}{5 \times 2} = -\frac{48}{10}. \]
- Convert \(-\frac{25}{2}\):
\[ -\frac{25}{2} = -\frac{25 \times 5}{2 \times 5} = -\frac{125}{10}. \]
Now, we can add the two fractions together:
\[ -\frac{48}{10} + \left(-\frac{125}{10}\right) = -\frac{48 + 125}{10} = -\frac{173}{10}. \]
Thus, the result of the operation is
\[ -\frac{173}{10}. \]