\( \frac{5}{2}b \cdot [ (1+\frac{2}{3})cd - [ (2+\frac{3}{4})c - \frac{10}{3} \cdot ( \frac{17c}{4} - \frac{23}{4}) + (4 + \frac{3}{8}c]) \cdot \frac{24}{5}d ] \)

= \( \frac{5}{2}b [ cd + \frac{2}{3}cd - [2c + \frac{3}{4}c - \frac{170c}{12} + \frac{230}{12} + 4c + \frac{3}{8}c] \cdot \frac{24}{5}d ] \)

= \( \frac{5}{2}b \cdot  [cd + \frac{2}{3}cd - \frac{48}{5}cd - \frac{72}{20}cd + \frac{4080}{60}cd - \frac{5520}{60}d - \frac{96}{5}cd - \frac{72}{40}cd] \)

= \( \frac{5}{2}bcd + \frac{10}{6}bcd - \frac{240}{10}bcd - \frac{360}{40}bcd + \frac{20400}{120}bcd - \frac{27600}{120}bd - \frac{480}{10}bcd - \frac{350}{80}bcd \)

= \( \frac{266}{3}bcd - 230bd \)