Where does the graph of y = ( 5 x 4 ) - ( x...

An inflection point on a graph is a point where the concavity changes. We'll look at the sign of the second derivative to investigate concavity:
${\displaystyle y=5x^4-x^5}$
${\displaystyle y\prime =20x^3-5x^4}$
${\displaystyle y\prime \prime =60x^2-20x^3=20x^2(3-x)}$
Obviously ${\displaystyle 20x^2}$ is always positive, so the sign of y'' is the same as the sign of ${\displaystyle 3-x}$.
Which is positive for ${\displaystyle x<3}$ and negative for ${\displaystyle x>3}$. At ${\displaystyle x=3}$ the concavity changes.
Because an inflection point is a point on a graph, we need:
when ${\displaystyle x=3}$, we get
${\displaystyle y=5\left(3^4\right)-3^5=5\left(3^4\right)-3\left(3^4\right)=2\left(3^4\right)=2\left(81\right)=162}$
The point (3, 162) in the only inflection point for the graph of ${\displaystyle y=5x^4-x^5}$