1. **State the problem:** We are given the function $f(x) = 5x - 7$ and need to evaluate $f(-3)$. 2. **Recall the formula:** The function $f(x)$ means for any input $x$, the output is calculated by multiplying $x$ by 5 and then subtracting 7. 3. **Substitute the value:** Replace $x$ with $-3$ in the function: $$f(-3) = 5(-3) - 7$$ 4. **Calculate step-by-step:** $$f(-3) = -15 - 7$$ 5. **Simplify:** $$f(-3) = -22$$ 6. **Final answer:** The value of $f(-3)$ is $-22$.