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

1. Evaluate $f(4)$: $f(4) = 5(4)^2 - 4$ $= 5(16) - 4$ $= 80 - 4 = 76$

2. Evaluate $f(-4)$: $f(-4) = 5(-4)^2 - 4$ $= 5(16) - 4$ $= 80 - 4 = 76$

3. Add the results: $f(4) + f(-4) = 76 + 76 = 152$

So, $f(4) + f(-4) = 152$.

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. How would the function change if it was $f(x) = 5x^2 + 4$?
3. What is the vertex of the parabola represented by $f(x) = 5x^2 - 4$?
4. How do you find the roots of the equation $f(x) = 0$?
5. What is the derivative of the function $f(x) = 5x^2 - 4$?

Tip: For any quadratic function $ax^2 + bx + c$, substituting $x$ with a positive or negative value yields the same result for the $x^2$ term because squaring a number makes it positive.