To determine the correct system of equations that represents the given situation, we need to translate the problem's conditions into mathematical equations.
1. We are told that the length of the sandbox (denoted by \( l \)) is 5 feet longer than twice the width (denoted by \( w \)). This translates into the equation:
[tex]\[
l = 2w + 5
\][/tex]
2. We also know that the total perimeter of the sandbox is 220 feet. The perimeter of a rectangle is given by the formula \( 2w + 2l \), which leads to the equation:
[tex]\[
2w + 2l = 220
\][/tex]
Now, putting these two equations together to form a system of equations, we have:
[tex]\[
\left\{
\begin{array}{c}
2w + 2l = 220 \\
l = 2w + 5
\end{array}
\right.
\][/tex]
Looking at the provided options, this system of equations corresponds to option C:
[tex]\[
\left\{
\begin{array}{c}
2w + 2l = 220 \\
l = 2w + 5
\end{array}
\right.
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{C} \)[/tex].
