  In this paper we obtain a parametric solution of the hitherto unsolved
diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$.
Further, we show, using elliptic curves, that there exist infinitely many
parametric solutions of the aforementioned diophantine equation, and they can
be effectively computed.
