Let [tex]x[/tex] be the length of the rectangle, and let [tex]y[/tex] be its width. The perimeter of a rectangle is the sum of all its side lengths:
[tex]P=2x+2y[/tex]
(since there are two sides of length [tex]x[/tex] and two sides of length [tex]y[/tex])
You know the perimeter is 18 meters, so the equation above is
[tex]18=2x+2y[/tex]
Now, you also know that the length of the rectangle is 5 meters longer than the width, which means [tex]x=y+5[/tex], or equivalently, [tex]x-y=5[/tex]. So you have two equations depending on [tex]x[/tex] and [tex]y[/tex]:
[tex]\begin{cases}2x+2y=18\\x-y=5\end{cases}[/tex]
From here, you could substitute the second equation into the first to get an equation only in terms of the width [tex]y[/tex]. Since [tex]x=y+5[/tex], you have
[tex]2(y+5)+2y=18[/tex]
and solve for [tex]y[/tex] from there (but you're not asked to do so).
