There are two ways for $ x $ to not be in the domain of $ g $: it can not be in the domain of $ f $, or it can be in the domain of $ f $ but not in the domain of $ f(f) $. In the first case, the denominator of $ f $ is zero, so $$2x-5=0\Rightarrow x=\frac{5}{2}.$$ For the second case, we see that the denominator of $ f(f(x)) $ is $ \frac{2}{2x-5}-5 $. If this is zero, we have $$5(2x-5)=2\Rightarrow 10x=27\Rightarrow x=\frac{27}{10}.$$ This is greater than $ \frac{5}{2} $. So the largest $ x $ not in the domain of $ g $ is $ \boxed{\frac{27}{10}} $.