Question 917518
OOPS!
I reversed the numbers.
What's inside the root is 

{{{-4+5x=5x-4}}} so for the 6th root to exist we need
{{{5x-4>=0}}}---->{{{x>=4/5}}}
So the interval is
[4/5,infinity).
  
For the fifth root the answer is still right.
  
OLD, WRONG ANSWER:
{{{root(6,-4x+5)}}} , being an even index root (6 is an even number),
is defined only when what's inside the root is positive or zero,
meaning {{{-4x+5>=0}}}<--->{{{5>=4x}}}<--->{{{5/4>=x}}} ,
so the domain is {{{"("}}}{{{-infinity}}}{{{","}}}{{{5/4}}}{{{"]"}}} .
 
{{{root(5,-4x+5)}}} , being an odd index root (5 is an odd number),
exists no matter what value {{{-4x+5}}} takes,
so the domain is {{{"("}}}{{{-infinity}}}{{{","}}}{{{infinity}}}{{{")"}}} .