ABC is a triangle in a plane with vertices $A(2, 3, 5), B(−1, 3, 2)$ and $C(λ, 5, µ).$ If the median through $A$ is equally inclined to the coordinate axes, then the value of $(λ^3+µ^3+5)$ is :

Question

$\begin{array}{1 1} (1)\; 1130 \\(2)\; 1348\\ (3)\; 676\\ (4)\; 1077 \end{array} $