1. **State the problem:** We need to find by how many orders of magnitude the severities of two earthquakes differ, one rated 5 and the other 4.7 on the Richter scale. 2. **Recall the formula:** The difference in earthquake severities on the Richter scale is given by the formula: $$\text{Difference} = 10^{(M_1 - M_2)}$$ where $M_1$ and $M_2$ are the magnitudes of the two earthquakes. 3. **Apply the values:** Here, $M_1 = 5$ and $M_2 = 4.7$, so: $$10^{(5 - 4.7)} = 10^{0.3}$$ 4. **Calculate the value:** Using the property of exponents and logarithms, $10^{0.3} \approx 2$ (since $10^{0.3} = e^{0.3 \ln 10} \approx e^{0.3 \times 2.3026} \approx e^{0.6908} \approx 2$). 5. **Interpretation:** The earthquake rated 5 is approximately 2 times more severe than the one rated 4.7, meaning they differ by about 2 orders of magnitude. **Final answer:** The severities differ by approximately $2$ orders of magnitude.