5) \( \lim _{x \rightarrow-3}(x+1)\left(x^{3}-3 x+6\right)= \)

To find the limit \( \lim _{x \rightarrow-3}(x+1)\left(x^{3}-3 x+6\right) \), we start by substituting \( x = -3 \): First, calculate \( x + 1 \) when \( x = -3 \): \[ -3 + 1 = -2. \] Next, calculate \( x^3 - 3x + 6 \) when \( x = -3 \): \[ (-3)^3 - 3(-3) + 6 = -27 + 9 + 6 = -12. \] Now, we can plug these values into the limit: \[ \lim _{x \rightarrow -3}(x+1)\left(x^{3}-3 x+6\right) = (-2)(-12) = 24. \] Thus, the answer is \( \boxed{24} \).