If we place 5 dots in a square of side length $s$, there must be at least two dots whose distance $d$ satisfies: $$ d < \frac{s}{\sqrt{2}} $$
(The user requested condition: "distance is smaller than square root of square ($s^2$)", which means $d < \sqrt{s^2}=s$. Since $\frac{s}{\sqrt{2}} \approx 0.707 s < s$, the condition is always met if the stronger Pigeonhole Principle holds.)