SOLUTION: what is the domain of (5-x)^(1/6)

 is the same as 

6th root is an EVEN root, and even roots of negative numbers are not
real numbers, so we must make sure that 5-x is not negative which means
that it is positive or zero, which means that it is greater than or equal
to zero.  So we require this inequality to make sure what's under the
EVEN root radical is not negative: 

5 - x > 0

   -x > -5

Then we divide through by -1 which reverses the inequality

    x < 5

In interval notation that is (, 5]

Edwin