Simplify 7 1/2×(7/8-5/24)

To simplify the expression \( 7 \frac{1}{2} \times \left( \frac{7}{8} - \frac{5}{24} \right) \), we can follow these steps:

1. **Convert the mixed number to an improper fraction**:
\[
7 \frac{1}{2} = \frac{15}{2}
\]

2. **Find a common denominator for the fractions**:
The common denominator for \( \frac{7}{8} \) and \( \frac{5}{24} \) is \( 24 \).

- Convert \( \frac{7}{8} \) to 24ths:
\[
\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
\]

- \( \frac{5}{24} \) is already in terms of \( 24 \):
\[
\frac{5}{24} = \frac{5}{24}
\]

3. **Subtract the fractions**:
\[
\frac{21}{24} - \frac{5}{24} = \frac{21 - 5}{24} = \frac{16}{24}
\]

4. **Simplify \( \frac{16}{24} \)**:
\[
\frac{16}{24} = \frac{2}{3} \quad \text{(by dividing numerator and denominator by 8)}
\]

5. **Multiply \( \frac{15}{2} \) by \( \frac{2}{3} \)**:
\[
\frac{15}{2} \times \frac{2}{3} = \frac{15 \times 2}{2 \times 3} = \frac{30}{6}
\]

6. **Simplify \( \frac{30}{6} \)**:
\[
\frac{30}{6} = 5
\]

Thus, the simplified result of \( 7 \frac{1}{2} \times \left( \frac{7}{8} - \frac{5}{24} \right) \) is

\[
\boxed{5}
\]