Algebra

First, let's combine all like terms. We get

$y=-5x^2-6x+10$

Now, the equation for the x value of the vertex is

$x=\frac{-b}{2a}$ for quadratics in the form of $ax^2+bx+c$

Thus, we have $x=\frac{-(-6)}{2(-5)} =- \frac{6}{10}$

Plugging in x into the equation for y, we have 

$y=\frac{59}{5}$

Thus the vertex is $\left(-\frac{3}{5},\:\frac{59}{5}\right)$

So our answer is $\left(-\frac{3}{5},\:\frac{59}{5}\right)$

Thanks! :)