jmc

We set the length to be $l$ and the width to $l+5$. We can write the problem as the inequality $l(l+5)\ge 500$. Distributing on the left-hand side, subtracting 500 from both sides, and factoring, we get $$\begin{array}{rl}l(l+5)& \ge 500\Rightarrow \\ l^2+5l-500& \ge 0\Rightarrow \\ (l+25)(l-20)& \ge 0.\end{array}$$The area is at least 500 square feet when the $l\le -25\text{ or }l\ge 20$. The dimensions can't be negative, so the smallest length possible while still having an area of at least 500 square ft is $20$ ft. Therefore, the width of the plot is $20+5=\boxed{25\text{ ft}}$.