The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and the plane $2x-2y+z=5$ is

Take $(a_1,b_1,c_1)=(3,4,5)$ and $(a_2,b_2,c_2)=(2,-2,1)$. 
Use $\cos \left(\frac{{\displaystyle \pi }}{{\displaystyle 2}}-\theta \right)=\frac{|a_1{a}_2+b_1{b}_2+c_1{c}_2|}{\sqrt{a_{{ }_1}^2+b_{{ }_1}^2+c_{{ }_1}^2}\sqrt{a_{{ }_2}^2+b_{{ }_2}^2+c_{{ }_2}^2}}$