I do not know how to solve it mathematically, I hope someone does and we can both learn.
I DO know at very small values , as x approaches zero, sin(x) ~~ x so the numerator becomes 5x as we approach zero 5x/x = 5 But I do not think that is a very good proof of your question.......
You can GRAPH sin(5x) / 5 and see it is true too.....still not a great proof.....
Anyone?