What you have labeled
$\chi^2_{\alpha/2}\approx 26.119$ is the value of a chisquare random variable
$X$ that has a probability of
$\alpha/2$ in the right tail. The correct function to use is the InverseCDF which gives the value of the chisquare random variable that has
$\alpha/2$ in the left tail. So you will need the following:
InverseCDF[ChiSquareDistribution[14], 0.05/2]
(* 5.62873 *)
InverseCDF[ChiSquareDistribution[14], 1 - 0.05/2]
(* 26.1189 *)
You get the wrong value because in your attachment you have
CDF[ChiSquareDistribution[14], (1 - 0.05)/2]
which should be
InverseCDF[ChiSquareDistribution[14], 1 - 0.05/2]
