Acute angle, in radians  between the lines whose slope is $2$ and the line which is perpendicular to the line $2x-y+5=0$ is

$\text{ The slope of the line }2x-y+5=0\text{ is }m=-\frac{a}{b}=2\text{, it is same as the slope of the first line. }$

Hence the angle between the line whose slope is 2 and the line which is perpendicular to the line $2x-y+5=0\text{ is }\frac{\pi }{2}=1.57$