The biquadratic Diophantine equation with five unknowns (X-Y) (x3+Y3) = 39(W2-Z2) P2 is analysed for its infinitely many non-zero distinct integral solutions. A few interesting properties among the values of x, y, z, w, p and special numbers namely, polygonal, Centered pyramidal, Jacobsthal numbers, and Four dimensional figurate numbers are presented.