5. The minimum distance from the lattice points (points with integer coordinates) to the line $y=\frac{5}{3} x+\frac{4}{5}$ is ( ).
(A) $\frac{\sqrt{34}}{170}$
(B) $\frac{\sqrt{34}}{85}$
(C) $\frac{1}{20}$
(D) $\frac{1}{30}$
(2000, National High School Mathematics Competition)
(Tip: The distance from a point to a line can be converted to $\frac{\sqrt{34}}{170}$. $25 x-$ $15 y+12|$. Since $x, y \in \mathbf{Z}$, then $|25 x-15 y+12|$ must be an integer. Its minimum value is 2. Therefore, the answer is (B).)