In math literature there is mention of the above topic. Even Euler and others have given parametric solutions (see Dickson, 1919). There are some parametric solutions on the internet (Stack Exchange, n.d.-a, n.d.-b, n.d.-c, n.d.-d, n.d.-e). In this paper the authors have provided alternate methods to find parametric solutions. While some authors have given solutions of degree three and higher, the present paper provides solutions of degree five and degree two.