Yes, the turning point is correct.

Your graph however is not... what is the actual graph...

Put x = 2. Then, y = -1/15, which is lower than the turning point. This means that the curve goes down from the turning point.

And this being an 'inverted' square function (ie like y = 1/x^2), you have some sort of 'volcano' shape.

See here:

http://www.wolframalpha.com/input/?i=+y%3D+\frac{1}{(x-5)(x%2B3)}

[And this is a pre-university question]