An algebra problem by Phudish Prateepamornkul

Algebra Level 3

$\begin{aligned} ax+by &=& 40 \\ ax^2+by^2 &=& 110 \\ ax^3+by^3 &=& 310 \\ ax^4+by^4 &=& 890 \end{aligned}$

Let $a,b,x,$ and $y$ be real variables satisfying the system of equations above.

Find the value of $ax^5+by^5$ .