Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x⁶ is unity and it has extrema at x = $-$1 and x = 1. If $\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1$, then $5.f(2)$ is equal to _________.