Find a cubic polynomial

f$($x$)=$ax$3+$bx$2+$cx$+$df$($x$)=$ax$3+$bx$2+$cx$+$d

that has horizontal tangents at the points $(-5,4)$ and $(2,-2).$

f$($x$)$f$($x$)=2243$x$3+1081$x$28081$x$118243$