Use logarithms to solve. (If there is no solution, enter NO SOLUTION.) \[ e^{r+5}-5=-31 \]

Step 1 ：Given the equation \(e^{r+5}-5=-31\)

Step 2 ：Add 5 to both sides of the equation to isolate the exponential term, resulting in \(e^{r+5}=-26\)

Step 3 ：Take the natural logarithm (ln) of both sides of the equation to get rid of the exponential term on the left side, resulting in \(r+5=\ln(-26)\)

Step 4 ：Subtract 5 from both sides to solve for r, resulting in \(r=\ln(-26)-5\)

Step 5 ：However, the natural logarithm of a negative number is undefined in the real number domain, which means that there is no real solution to the equation.

Step 6 ：Final Answer: \(\boxed{\text{NO SOLUTION}}\)