2 1/2 - (2/5 + 3/4) ÷ (5/8 × 2/3)

$$\left(\frac{5}{8} \times \frac{2}{3}\right) = \frac{5 \times 2}{8 \times 3} = \frac{10}{24}$$

Simplify the fraction:

$$\frac{10}{24} = \frac{10 \div 2}{24 \div 2} = \frac{5}{12}$$

Now the expression is $\frac{5}{2} - \frac{23}{20} \div \frac{5}{12}$.
To divide by a fraction, multiply by its reciprocal:

$$\frac{23}{20} \div \frac{5}{12} = \frac{23}{20} \times \frac{12}{5}$$ $$\frac{23 \times 12}{20 \times 5} = \frac{23 \times (4 \times 3)}{(4 \times 5) \times 5} = \frac{23 \times 3}{5 \times 5} = \frac{69}{25}$$

Now the expression is $\frac{5}{2} - \frac{69}{25}$.
Find a common denominator, which is 50:

$$\frac{5}{2} - \frac{69}{25} = \frac{5 \times 25}{2 \times 25} - \frac{69 \times 2}{25 \times 2}$$ $$= \frac{125}{50} - \frac{138}{50}$$ $$= \frac{125 - 138}{50} = \frac{-13}{50}$$

The final answer is $-\frac{13}{50}$.