We set the length to be $ l $ and the width to $ l+5 $. We can write the problem as the inequality $ l(l+5)\ge500 $. Distributing on the left-hand side, subtracting 500 from both sides, and factoring, we get \begin{align*} l(l+5)&\ge500 \quad \Rightarrow \\ l^2+5l-500&\ge 0 \quad \Rightarrow \\ (l+25)(l-20)&\ge 0.\end{align*}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}} $.