In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:

Comparing with the given equation, we have a = -5, b = -270 and c = -520.
Now, let's calculate the x-coordinate of the vertex using the formula below:

Using this value of x in the equation, we can find the y-coordinate of the vertex:

Therefore the vertex is located at (-27, 3125).