Let's solve for $f'(x)$ using the four-step process for the given function $f(x) = 5x^2 - 3x$.

Step-by-step differentiation:

1. Given function: $f(x) = 5x^2 - 3x$

2. Differentiate each term separately:

   • The derivative of $5x^2$ with respect to $x$: $\frac{d}{dx} (5x^2) = 2 \times 5x^{2-1} = 10x$
   • The derivative of $-3x$ with respect to $x$: $\frac{d}{dx} (-3x) = -3$

3. Final derivative $f'(x)$: $f'(x) = 10x - 3$

So, the correct answer is B. $10x - 3$.

Do you want further details on the steps? Here are some related questions to practice:

1. What is the derivative of $6x^3 - 4x^2 + x$?
2. How do you differentiate a constant term like $5$?
3. What is the power rule for differentiation?
4. Can you explain the four-step process in calculus?
5. How do you apply the product rule in differentiation?

Tip: When differentiating powers of $x$, remember to multiply by the exponent and reduce the power by one.