Observations on the homogeneous quintic equation with four unknowns x⁵ - y⁵ = 2z⁵ + 5(x+y)(x²-y²)w²

We obtain infinitely many non-zero integer quadruples (x, y, z, w) satisfying the quintic equation with four unknowns x⁵ - y⁵ = 2z⁵ + 5(x+y)(x²-y²)w². Various interesting properties among the values of x, y, z and w are presented.