1. **State the problem:** Solve for $y$ in the equation $$e^{y + 5} = 5$$ and round the answer to the nearest hundredth. 2. **Recall the formula and rules:** To solve for $y$ when it is in the exponent, use the natural logarithm (ln), which is the inverse of the exponential function with base $e$. 3. **Apply the natural logarithm to both sides:** $$\ln\left(e^{y + 5}\right) = \ln(5)$$ 4. **Use the logarithm power rule:** $$y + 5 = \ln(5)$$ 5. **Isolate $y$:** $$y = \ln(5) - 5$$ 6. **Calculate the value:** $$\ln(5) \approx 1.6094379124341003$$ So, $$y \approx 1.6094379124341003 - 5 = -3.3905620875658997$$ 7. **Round to the nearest hundredth:** $$y \approx -3.39$$ **Final answer:** $$\boxed{y \approx -3.39}$$