Why can't you have more turning points than the degree? I get that each degree can correspond to a factor.   $x^5=(x+a)(x+b)(x+c)(x+d)(x+e)$ and that results in 4 turning points, so the graph can "turn around" and hit the next zero.    Why can't a curve have more turning points than zeros?   
In the graph below, there are 4 roots, so degree is 4, but way more turning points than 4.    What gives?   Are those additional turning points represented by imaginary roots?


You can use calculus to prove this. There is a "turning point" when the derivative of the polynomial is $0$ and the second derivative is non-$0.$ The derivative of your quintic function is a quartic function. There can be a maximum of $4$ zeroes in a quartic polynomial, so there can be at most $4$ "turning points," if the second derivative at each of these points is non-zero.
