To evaluate the function $f(x) = -2x^2 + 7x + 5$ at $x = 0$, substitute $x = 0$ into the function:

$f(0) = -2(0)^2 + 7(0) + 5$

Simplifying the expression:

$f(0) = -2(0) + 0 + 5 = 5$

So, $f(0) = 5$.

Would you like more details or have any questions?

Here are some related questions you might consider:

1. What is $f(1)$ for the same function?
2. What are the x-intercepts of the function $f(x)$?
3. How does the negative coefficient of $x^2$ affect the shape of the parabola?
4. What is the maximum or minimum value of $f(x)$?
5. How does the function change if the coefficient of $x$ is altered?

Tip: When dealing with quadratic functions, the sign of the coefficient of $x^2$ determines whether the parabola opens upwards (positive) or downwards (negative).