Should I solve for $a$ in this equation?

Question

If $\dfrac{a^2 -1}a = 5$ then find the value of $\dfrac{a^6 - 1}{a^3}$.

Answer 1

Hint: Contest math loves the expressions $a\pm\frac 1a$. You should recognize your left side as one of these. Powers of them are quite simple because terms combine. You are looking for $a^3-\frac 1{a^3}$. How can you get something that looks somewhat like that?