Okay, let's see. I need to find the value of the function f(x) at x = -2. The function is given as f(x) = 5x² + 3x + 4. Hmm, that seems straightforward. Let me make sure I remember how to substitute a value into a quadratic function. 

First, I should recall that to evaluate a function at a specific point, I just replace every instance of x in the function with that value. So for f(-2), I need to substitute x with -2 in the equation. Let me write that out step by step to avoid mistakes.

Starting with the original function:
f(x) = 5x² + 3x + 4

Substitute x = -2:
f(-2) = 5*(-2)² + 3*(-2) + 4

Now, let's compute each term one by one. The first term is 5 times (-2) squared. Squaring a negative number gives a positive result, so (-2)² is 4. Then, 5 multiplied by 4 is 20. Okay, that's the first part.

The second term is 3 times (-2). Multiplying 3 and -2 gives -6. So that term is -6.

The third term is just a constant, 4. So adding that to the previous results.

Now, putting it all together:
20 (from the first term) + (-6) (from the second term) + 4 (from the third term)

Let me compute that step by step. 20 minus 6 is 14. Then 14 plus 4 is 18. So f(-2) should be 18. 

Wait, let me double-check my calculations to make sure I didn't make any arithmetic errors. It's easy to mix up signs or multiply wrong. 

First term: (-2) squared is 4, multiplied by 5 is 20. Correct. 

Second term: 3 times -2 is indeed -6. Correct. 

Third term: 4. Correct. 

Adding them up: 20 -6 +4. Let's do the addition step carefully. 20 -6 is 14, then 14 +4 is 18. Yep, that seems right. 

Alternatively, maybe I can compute it all at once to verify. Let's compute each term again:

5*(-2)² = 5*(4) = 20

3*(-2) = -6

4 remains 4.

So 20 -6 +4. 

20 minus 6 is 14. 14 plus 4 is 18. Correct. 

I think that's solid. Let me check another way. Maybe expand the expression again. 

f(-2) = 5*(-2)^2 + 3*(-2) + 4

Calculating exponents first: (-2)^2 is 4. Then multiply by 5: 20. Then 3*(-2) is -6. Then add 4. So 20 -6 +4. 

Same result. 

Alternatively, maybe compute all terms together:

5*(-2)^2 = 5*4=20

3*(-2) = -6

4 is 4

Adding them: 20 + (-6) +4. 

Which is 20 -6 +4. 20-6 is 14, 14+4=18. Yep. 

I don't see any errors here. So the answer should be 18. 

Wait, just to be absolutely thorough, let me write out the entire calculation again:

5*(-2)^2 = 5*4 = 20

3*(-2) = -6

4 remains 4

Total: 20 + (-6) +4 = 20 -6 +4 = 18. 

Yes, that's correct. 

Alternatively, maybe use a different order of operations. Let's compute 5*(-2)^2 first. 

(-2)^2 is 4. 5*4 is 20. Then 3*(-2) is -6. Then add 4. So 20 -6 +4. 

Same as before. 

Alternatively, maybe compute all the terms as decimals. Wait, but they are all integers here. 

Alternatively, maybe use a different approach. Let's compute each term again:

First term: coefficient of x² is 5, x is -2. So 5*(-2)^2. 

Compute the exponent first: (-2)^2 = 4. Then multiply by 5: 5*4=20. 

Second term: coefficient of x is 3, so 3*(-2) = -6. 

Third term: constant term is 4. 

Adding all together: 20 + (-6) +4. 

Which is 20 -6 +4. 

20-6 is 14. 14+4 is 18. 

Everything checks out. 

I think that's solid. No mistakes detected. So the answer is 18.
Therefore, the value of $f(-2)$ is $\boxed{18}$.
</think>