The possible solution follows, shown in several steps:
log1/5((x2+x)/(x2-x)) = -2
(x2+x)/(x2-x) = (1/5)-2 = 25
(x2+x) = 25(x2-x),
has a trivial solution x=0 and a second non-trivial one x=26/24=13/12 (it could be solved using online Quadratic Equation Solver: http://examn8.com/QuadraticEquations.aspx).
Trivial solution x=0 should be discarded because it leads to a logarithm of zero, thus only one solution x=13/12 is valid.
Hope this will help.