Approximately,
\[
\begin{alignedat}{4}
A^\prime_{\mathbf{5}}&{}\approx{}&0.954027186633&{}:{}&0.016827217576&{}:{}&0.029145595791&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.571630050544&{}:{}&-0.561722341219&{}:{}&0.990092290675&,\\C^\prime_{\mathbf{5}}&{}\approx{}&1.366025403784&{}:{}&1.366025403784&{}:{}&-1.732050807569&,
\\
A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.805985572786&{}:{}&0.006984824160&{}:{}&0.187029603054&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.959040579625&{}:{}&0.033244911755&{}:{}&0.007714508620&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.943092357278&{}:{}&0.000283315696&{}:{}&0.056624327026&,
\\
A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.799605434820&{}:{}&0.785746369477&{}:{}&1.013859065343&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&1.004748554226&{}:{}&0.017721845633&{}:{}&-0.022470399859&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.986954739918&{}:{}&-0.017106274714&{}:{}&0.030151534796&,
\\
A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.082262332300&{}:{}&1.082262332300&,\\B^*_{\mathbf{5}}&{}\approx{}&0.814313139868&{}:{}&0.000000000000&{}:{}&0.185686860132&,\\C^*_{\mathbf{5}}&{}\approx{}&1.017638090205&{}:{}&-0.017638090205&{}:{}&0.000000000000&.
\end{alignedat}
\]