Given,

The plane passes through $\left(-2,1,3\right)$ and is perpendicular to vector $3\hat{i}+\hat{j}+5\hat{k}$

$\therefore$ Equation of plane is $3x+y+5z=\lambda$ passes through $-2,1,3$

So, $3x+y+5z=\lambda$ passes through $-2,1,3$

$\therefore 3\times \left(-2\right)+1+5\times 3=\lambda$

$\Rightarrow -6+1+15=\lambda \Rightarrow 10=\lambda$

$\therefore$ Equation of plane is $3x+y+5z=10$

Now on comparing with $ax+by+cz+d=0$

We get $a=3, b=1, c=5 \& d=-10$,

So the value of $\frac{a+b}{c+d}=\frac{3+1}{5-10}=\frac{-4}{5}$