I have to find "The open intervals on which f is concave upward and downward"

I put the image as an attachment

I know inflection points at x=2, x=4,x=5.

I said it was concave upward (2,4) and concave downward on (0,2). The inflection point is where concavity begins/ends right? I can't seem to get the right answer.Any help would be great