The two equations combined yields $x\times 4^x=32$ . Since for negative $x$ the value of the L. H. S. is negative, the curve $y=x\times 4^x$ can not intersect the line $y=32$ . For positive $x$ , the function $y=x\times 4^x$ is increasing and at $x=0$ , $y=0<32$ . Hence it will intersect the line $y=32$ only once in this domain. This will happen when $x=2$ , and hence $y=5-2x=1$ .

So $x+y=2+1=\boxed 3$ .

By brute force

$\text{At } x = 2, y = 1 \text{ in both the equations.}$

$\text{So, }\color{#3D99F6}{\boxed{x + y = 3}}$