1. The problem is to multiply two fractions: $\frac{7}{8} \times \frac{5}{2}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$\nThis means you multiply the numerators together and the denominators together.\n\n3. Applying the formula to our problem:\n$$\frac{7}{8} \times \frac{5}{2} = \frac{7 \times 5}{8 \times 2} = \frac{35}{16}$$\n\n4. The fraction $\frac{35}{16}$ is an improper fraction (numerator larger than denominator). We can convert it to a mixed number:\n$$35 \div 16 = 2 \text{ remainder } 3$$\nSo,\n$$\frac{35}{16} = 2 \frac{3}{16}$$\n\n5. Therefore, the final answer is $\frac{35}{16}$ or $2 \frac{3}{16}$.