Question 113
Determine all triple of real numbers $(a, b, c)$, which satisfy the following system of equations: $$
\left\{
\begin{array}{l}
a^{5} = 5 b^{3} - 4 c \\
b^{5} = 5 c^{3} - 4 a \\
c^{5} = 5 a^{3} - 4 b
\end{array}
\right.
$$
\left\{
\begin{array}{l}
a^{5} = 5 b^{3} - 4 c \\
b^{5} = 5 c^{3} - 4 a \\
c^{5} = 5 a^{3} - 4 b
\end{array}
\right.
$$