Answer
$d = 1.47~m$
Work Step by Step
To be exactly in phase at the detector, the path difference should be $0.500~\lambda$, since the reflection shifts the sound wave by $0.500~\lambda$
Then the path length from the source to the flat surface must be $\frac{L}{2}+\frac{\lambda}{4}$:
We can find the distance from the source to the flat surface:
$\frac{L}{2}+\frac{\lambda}{4} = 5.00~m+\frac{0.850~m}{4} = 5.2125~m$
We can find $d$:
$d = \sqrt{(5.2125~m)^2-(5.00~m)^2} = 1.47~m$
