The perimeter of a rectangle is equal to two times the sum of the length and the width.
[tex]P=2(l+w)[/tex]
Rectangle A:
[tex]l=3x+2 \\ w=2x-1 \\ \\
P_A=2(3x+2+2x-1)=2(5x+1)=10x+2[/tex]
Rectangle B:
[tex]l=x+5 \\ w=5x-1 \\ \\
P_B=2(x+5+5x-1)=2(6x+4)=12x+8[/tex]
The perimeter of rectangle B minus the perimeter of rectangle A:
[tex]P_B - P_A=12x+8-(10x+2)=12x+8-10x-2=\boxed{2x+6}[/tex]