1. **Problem statement:** Given the functions $f(x) = x^2 - 5x$ and $g(x) = x - 5$, find the degree of each function and prove that $f(5) = g(5) = 0$. 2. **Degree of a polynomial:** The degree is the highest power of $x$ in the polynomial. 3. **Degree of $f(x)$:** The highest power of $x$ in $f(x) = x^2 - 5x$ is 2, so degree of $f(x)$ is 2. 4. **Degree of $g(x)$:** The highest power of $x$ in $g(x) = x - 5$ is 1, so degree of $g(x)$ is 1. 5. **Evaluate $f(5)$:** Substitute $x=5$ into $f(x)$: $$f(5) = 5^2 - 5 \times 5 = 25 - 25 = 0$$ 6. **Evaluate $g(5)$:** Substitute $x=5$ into $g(x)$: $$g(5) = 5 - 5 = 0$$ 7. **Conclusion:** Both $f(5)$ and $g(5)$ equal zero, proving the statement.