$letf\left(x\right)=\{\begin{array}{l}{x}^2-3x\le -5\\ x+p-5<x<-1\\ (q-7)(|1-x|+|1+x|),-1\le x\le 1\\ x+61<x<5\\ 3-x^{2}x\ge 5\end{array}$

If $f\left(x\right)$  is an  odd function then the value of $(p+q)$ , is

$f(-x)=\left\{\begin{array}{l}{x}^2-3,x\ge 5\\ -x+p,1<x<5\\ (q-7)(|1+x|+|1-x|),-1\le x\le 1\\ -x+6;-5<x<-1\\ 3-x^{2}x\ge -5\end{array}\right\}$

$f\left(x\right)+f(-x)=\{\begin{array}{l}0,x\le -5\\ p+6,-5<x<-1\\ +2(q-7)(|1-x|+|1+x|)-1\le x\\ p+b,1<x<5\\ 0x\ge 5\end{array}$

For  $f\left(x\right)$ to be an odd function

$f\left(x\right)+f(-x)=0\forall x\in R$

$p=-6q=7$

$p+q=1$