Given the function $f(x) = 5x^2 - 3$, we want to evaluate $f(4) + f(-4)$.

1. Evaluate $f(4)$: $f(4) = 5(4)^2 - 3$ $= 5(16) - 3$ $= 80 - 3 = 77$

2. Evaluate $f(-4)$: $f(-4) = 5(-4)^2 - 3$ $= 5(16) - 3$ $= 80 - 3 = 77$

3. Add the results: $f(4) + f(-4) = 77 + 77 = 154$

So, $f(4) + f(-4) = 154$.

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. What is the value of $f(0)$?
2. What happens if you evaluate $f(2) + f(-2)$?
3. How do you find the vertex of the function $f(x) = 5x^2 - 3$?
4. What is the axis of symmetry for the function $f(x) = 5x^2 - 3$?
5. How would the function change if it was $f(x) = 5x^2 + 3$?

Tip: In a quadratic function $ax^2 + bx + c$, the output values for $f(x)$ are symmetric about the y-axis, meaning $f(x) = f(-x)$ when $b = 0$.