If c - d = c + d5 = cd3 and c, d ≠ 0 then what is the value of cd?

Answer: Option B

$$\begin{array}{rl}& \because c-d=\frac{c+d}{5}=\frac{cd}{3}\\ & \Rightarrow 5c-5d=c+d\\ & \Rightarrow 4c=6d\\ & \Rightarrow \boxed{\frac{c}{d}=\frac{3}{2}}\\ & \Rightarrow c=\frac{3}{2}d......\left(1\right)\\ & \because \frac{c+d}{5}=\frac{cd}{3}\\ & \Rightarrow \frac{\frac{3}{2}d+d}{5}=\frac{\frac{3}{2}{d}^2}{3}\\ & \Rightarrow \frac{5d}{2}\times \frac{1}{5}=\frac{1}{2}{d}^2\\ & \Rightarrow d=1\\ & \text{From equation }\left(1\right)\\ & \boxed{c=\frac{3}{2}}\\ & \therefore \boxed{cd=\frac{3}{2}}\end{array}$$