Seeing a car in 5 minutes from the 20-minute odds

On a quiet road, the probability of seeing at least one car during any $20$-minute window is $\tfrac{609}{625}$. Assuming cars pass at a constant average rate (so non-overlapping windows are independent), what is the probability of seeing at least one car in a $5$-minute window?

$3/5$. No car for $20$ minutes means no car in four independent $5$-minute windows: $q^4=1-\tfrac{609}{625}=\tfrac{16}{625}$, so $q=\tfrac25$ and the answer is $1-\tfrac25$.