5. Given the function $f(x)=x^{2}+(a+1)^{2}+|x+a+1|$ has a minimum value $y^{\prime}>3$. Find the range of the real number $a$.

保留了原文的换行和格式。
(Solution: $a \leq$
$$\frac{-1-\sqrt{6}}{2} \text { or } a>\frac{\sqrt{2}}{2} \text { ) }$$