Answer
False
Explanation:
You can find the X value of the vertex by the formula: b/(-2a)
In order to understand who is 'b' and 'a', you have to think about the generic quadratic function:
f(x)=ax^2 +bx+c
So, in our case, b=+2 and a=-5
b/(-2a)= 2/(-1)(-10)=1/5
Than, the first derivate of f(x) gives you the value of a stationary point. It could be a maximum or a minimum
f'(x)= -10x +2
f'(x)=0 when x=1/5
So the X coordinate is the same.
But you have to verify if it is (or not) a minimum.
f'(x) is positive for x<1/5 and negative for x>1/5
Thus, f(x) is growing for x<1/5 and it is decreasing for x>1/5
x=1/5 is the vertex, but it isn't a minimum