5. Find the smallest positive value of the expression $x+y$ for all pairs of numbers ( $x ; y$ ) that satisfy the equation $(\tan x-2)(\tan y-2)=5$.

翻译完成，保留了原文的格式和换行。
Answer: $(x+y)_{\min }=\pi-\operatorname{arctg} \frac{1}{2}$.