Consider the two sets: $A=\{m\in R$ : both the roots of  $x^2-(m+1)x+m+4=0$ are real} and $B=[-3,5)$ . Which of the following is not true?

(a): We have,  $A=\{m\in R$ : Both the roots of $x^2-(m+1)x+m+4=0$  are real $\}$ 
$\because$ Roots of $x^2-(m+1)x+m+4=0$ are real
$$\begin{gathered} \therefore D\ge 0 \\ \Rightarrow {(m+1)}^2-4(m+4)\ge 0\Rightarrow m^2+1+2m-4m-16\ge 0 \\ \Rightarrow m^2-2m-15\ge 0\Rightarrow m^2-5m+3m-15\ge 0 \\ \Rightarrow (m-5)(m+3)\ge 0\Rightarrow m\in (-\infty ,-3]\cup [5,\infty ) \\ \Rightarrow A=(-\infty ,-3]\cup [5,\infty ) and B=[-3,5) \end{gathered}$$
So,  $A-B=(-\infty ,-3)\cup [5,\infty )$

$A\cap B=\{-3\}$
$B-A=(-3,5)$
$A\cup B=(-\infty ,-3]\cup [5,\infty )\cup [-3,5)=(-\infty ,\infty )=R$