There are only two unknowns!?

Algebra Level 4

\[\large{ \begin{cases} ax + by = 8 \\ ax^2 + by^2 = 14 \\ ax^3 + by^3 = 62 \\ ax^4 + by^4= 146 \\ \end{cases}} \]

If \(a,b,x\) and \(y\) are real number satisfying the system of equations above, find \(ax^5 + by^5 \).

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