1. Given:

   • Spring constant: $k = 5 \times 10^3\,\text{N/m}$
   • Initial stretch: $x_1 = 5\,\text{cm} = 0.05\,\text{m}$
   • Further stretch: $5\,\text{cm}$, so final stretch $x_2 = 10\,\text{cm} = 0.10\,\text{m}$

2. **Work required to stretch a spring from $x_1$ to $x_2$: ** $W = \frac{1}{2}k\left(x_2^2 - x_1^2\right)$

3. Substitute the values: $W = \frac{1}{2}(5 \times 10^3)\left((0.10)^2 - (0.05)^2\right)$

4. Calculate the squares: $(0.10)^2 = 0.01, \quad (0.05)^2 = 0.0025$ $0.01 - 0.0025 = 0.0075$

5. Now compute: $W = 2500 \times 0.0075 = 18.75\,\text{J}$

6. Since $1\,\text{J} = 1\,\text{N-m}$, $W = 18.75\,\text{N-m}$

7. Option check:

   • A: $12.50\,\text{N-m}$ ❌
   • B: $18.75\,\text{N-m}$ ✅
   • C: $25.00\,\text{N-m}$ ❌
   • D: $625\,\text{N-m}$ ❌

Therefore, the correct answer is B.