Sketch a right triangle with angle adjacent to a side of length 5. The hypotenuse has a length of x. So we know that
Thus the sine of this angle is
So your derivative is
which is (almost) correct.
A better way to approach this is to use
So the chain rule says:
which is again (almost) correct.
Why are neither of these answers quite correct? They work when x is positive. I leave it to you to find out what happens if x is negative. The correct answer is