$X + Y$

Let $x,y \geq 1$ . From the first relation, we deduce : $x = y+5$ Therefore : $x+y = 2y+1$ This is minimized for $y=1$ and thus the minimal value is: $2*1+5 = 7$

$x-y=5$

as we need the least possible value of , $x+y$ ,

we can do, $6-1=5$ ............[least possible value according to the condition]

so, $x+y=6+1=7$