ОДЗ: sin 5x≠cos 5x; 5x≠π/4+πm; x≠π/20+πm/5
sin^2 5x-sin 5x cos 5x=sin^2 5x+cos^2 5x;
cos^2 5x+sin 5x cos 5x=0;
cos 5x(cos 5x+sin 5x)=0;
cos 5x=0 (⇒5x=π/2+πn; x=π/10+πn/5 ∈ ОДЗ) или cos 5x+sin 5x=0;
tg 5x = -1; 5x=-π/4+πk; x= - π/20+ πk/5 ∈ОДЗ
Ответ: π/10+πn/5; - π/20+ πk/5; n,k∈Z