1. The problem gives the equation $17_r = 5$ and asks to find $r$. 2. The notation $17_r$ means the number 17 in base $r$. 3. In base $r$, the number $17_r$ is interpreted as $1\times r + 7$. 4. We are given that $1 \times r + 7 = 5$. 5. Simplify the equation: $r + 7 = 5$. 6. Subtract 7 from both sides: $r = 5 - 7$. 7. Calculate the right side: $r = -2$. 8. However, a base $r$ must be an integer greater than the largest digit (which is 7 here) and positive. 9. Since $r = -2$ is invalid, the equation cannot hold true with $r$ as a base system. Final answer: The given equation $17_r=5$ has no valid base $r$ satisfying it under normal base rules.