1. **State the problem:** We need to evaluate the function $f(x) = 5x^2 + 4x$ at $x = a$ and simplify the expression. 2. **Write the function with the given input:** Substitute $x$ with $a$ in the function: $$f(a) = 5a^2 + 4a$$ 3. **Simplify the expression:** Since $5a^2$ and $4a$ are unlike terms (one is quadratic, the other linear), they cannot be combined further. So the simplified form is: $$f(a) = 5a^2 + 4a$$ 4. **Final answer:** The value of the function at $x = a$ is: $$\boxed{5a^2 + 4a}$$