Evaluate the first term: (-(13)/(4) x (5)/(6)).

$\left(-\frac{13}{4} \times \frac{5}{6}\right)$.
Multiply the numerators and the denominators:

$$-\frac{13}{4} \times \frac{5}{6} = -\frac{13 \times 5}{4 \times 6} = -\frac{65}{24}$$

$\left(\frac{9}{2} \div \frac{3}{4}\right)$.
To divide by a fraction, multiply by its reciprocal:

$$\frac{9}{2} \div \frac{3}{4} = \frac{9}{2} \times \frac{4}{3}$$

Simplify before multiplying:

$$\frac{9}{3} \times \frac{4}{2} = 3 \times 2 = 6$$

$\left(\frac{5}{8} \times \frac{-6}{15}\right)$.
Multiply the numerators and the denominators. Simplify by canceling common factors:

$$\frac{5}{8} \times \frac{-6}{15} = \frac{5}{15} \times \frac{-6}{8} = \frac{1}{3} \times \frac{-3}{4} = -\frac{1 \times 3}{3 \times 4} = -\frac{1}{4}$$

The original expression becomes:

$$-\frac{65}{24} - 6 + \left(-\frac{1}{4}\right)$$ $$-\frac{65}{24} - 6 - \frac{1}{4}$$

To combine these, find a common denominator, which is 24.
Convert 6 to a fraction with denominator 24:

$$6 = \frac{6 \times 24}{1 \times 24} = \frac{144}{24}$$

Convert $-\frac{1}{4}$ to a fraction with denominator 24:

$$-\frac{1}{4} = -\frac{1 \times 6}{4 \times 6} = -\frac{6}{24}$$

Now substitute these back into the expression:

$$-\frac{65}{24} - \frac{144}{24} - \frac{6}{24}$$

Combine the numerators:

$$\frac{-65 - 144 - 6}{24} = \frac{-209 - 6}{24} = \frac{-215}{24}$$

The final answer is $-\frac{215}{24}$.