To find the value of $f(5)$ for the function $f(x) = 3x^2 + 2x - 1$, we will substitute $x = 5$ into the function and calculate the result.

Given: $f(x) = 3x^2 + 2x - 1$

We need to find $f(5)$: $f(5) = 3(5)^2 + 2(5) - 1$

First, calculate $5^2$: $5^2 = 25$

Next, multiply by 3: $3 \times 25 = 75$

Now, calculate $2(5)$: $2 \times 5 = 10$

Add these results together: $75 + 10 = 85$

Finally, subtract 1: $85 - 1 = 84$

Thus, the value of $f(5)$ is: $f(5) = 84$

The correct answer is: $\boxed{84}$

Do you want more details or have any questions?

Here are some related questions you might consider:

1. What is the value of $f(2)$ for the same function?
2. How do you find the vertex of the parabola represented by $f(x)$?
3. What is the value of $f(-3)$?
4. How do you determine the x-intercepts of the function $f(x)$?
5. What are the steps to find the derivative of $f(x)$?
6. What is the significance of the coefficient of $x^2$ in $f(x)$?
7. How can you determine if the function $f(x)$ has any symmetry?
8. How would you graph the function $f(x)$ on a coordinate plane?

Tip: Always check your calculations step-by-step to avoid errors and ensure accuracy.