"The length is 5 inches more than five times the width" can be expressed as
[tex]l=5+5w[/tex]The perimeter is 262 inches.
So, we have to use the perimeter formula to find the length and width
[tex]\begin{gathered} P=2(l+w) \\ 262=2(l+w) \\ l+w=131 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} l+w=131 \\ 5+5w+w=131 \\ 6w=131-5 \\ w=\frac{126}{6} \\ w=21 \end{gathered}[/tex]Now, we find the length
[tex]l=5+5w=5+5\cdot21=5+105=110[/tex]