Answer 2: No solutions.
sin(ex)=5x+5-x.
When x≥0 the right side has a minimum value of 2 (when x=0). When x=1, it's 5.2.
When x<0 the right side has the same values since 5|x|+5-|x|=5-|x|+5|x|. In other words, if x=-1, the right side is 5.2.
The sine function cannot exceed 1 so the left side can never equal the right side.