in the positive integer unknowns x > k and y > x. In particular, the equation
has infinitely many solutions when k = l = 1 (see also [3]), and no solutions when
k = l = 2 or 3 (see also [1]). Moreover, when k = l > 3, it has finitely many
solutions. However, for the case k = l = 5, the authors only got one solution
(x, y) = (14, 15) through a computer search with x ≤ 300. In this paper, we will
completely solve the equation