For the first copper rod:
\(L_0 = 5 \, \text{m} = 5000 \, \text{mm}, \quad \Delta T = 10 \, \text{°C}, \quad \Delta L = 1 \, \text{mm}\)
Coefficient of linear expansion \( \alpha \):
\(\alpha = \frac{1 \, \text{mm}}{5000 \, \text{mm} \cdot 10} = \frac{1}{50000} \, \text{mm}^{-1}\)

For the second copper rod:
\(L_0 = 2.5 \, \text{m} = 2500 \, \text{mm}, \quad \Delta T = 5 \, \text{°C}\)
Expansion:
\(\Delta L = L_0 \cdot \alpha \cdot \Delta T = 2500 \, \text{mm} \cdot \frac{1}{50000} \, \text{mm}^{-1} \cdot 5 = 0.25 \, \text{mm}\)

The second copper rod will expand by: \(0.25 \, \text{mm}\)