Answer
$$ (\frac{1}{2},\frac{23}{4})$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$5\left(x^2-x+\frac{7}{5}+\left(-\frac{1}{2}\right)^2-\left(-\frac{1}{2}\right)^2\right) \\ 5\left(\left(x-\frac{1}{2}\right)^2+\frac{7}{5}-\left(-\frac{1}{2}\right)^2\right) \\ 5\left(x-\frac{1}{2}\right)^2+\frac{23}{4}$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (\frac{1}{2},\frac{23}{4})$$
