Question 106297
Take a step back. 
It's tempting to just apply to rules and look for a solution. 
For the problem to have a solution, both log arguments (x-5) and (1-x) must be greater than zero
1.{{{(x-5)>0}}}
2.{{{(1-x)>0}}}
From 1., we get
{{{x>5}}} 
From 2., we get 
{{{x<1}}}
You cannot satisfy both condition since there is no x such that 
{{{x<1}}} and {{{x>5}}}.
No solution.