Rewrite the formula, putting $-2$ everywhere you see $x$. Use parentheses around $-2$ when you substitute into $x^2$ and $-3x$.

After substituting, do the exponent first, then the multiplications, and finally add all the terms together. Pay close attention to the negative signs in $(-2)^2$ and in $-3(-2)$.

Once you have three numbers (from $4x^2$, $-3x$, and $+5$), add them carefully. If your total does not come from adding three positive numbers, recheck your signs.

In Desmos, type the expression 4(-2)^2 - 3(-2) + 5 exactly as written (with parentheses around -2). The value that Desmos outputs for this expression is the value of $g(-2)$.

The function is defined by $g(x)=4x^2-3x+5$. The expression $g(-2)$ means: take the formula for $g(x)$ and replace every $x$ with $-2$, then simplify.

Write the expression for $g(-2)$ by substituting $-2$ for $x$:

Be sure to include parentheses around $-2$ so the square applies to the entire negative number.

First, calculate the square:

Now multiply:

So the expression becomes:

Add the numbers step by step:

So $g(-2)=27$, which corresponds to answer choice D.